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References

  1. Bertin, M.J., Decomps-Guilloux, A., Grandet-Hugot, M., Pathiaux-Delefosse, M., and Schreiber, J.P.: Pisot and Salem Numbers, Birkhäuser, 1992.

    MATH  Google Scholar 

  2. Boyd, D.W.: ‘Small Salem numbers’, Duke Math. J. 44 (1977), 315–328.

    MathSciNet  MATH  Google Scholar 

  3. Meyer, Y.: Algebraic numbers and harmonic analysis, North-Holland, 1972.

    MATH  Google Scholar 

  4. Mossinghoff, M.J.: Small Salem numbers, web page: http://www.math.ucla.edu/~mjm/lc/lists/SalemList.html, 1998.

    Google Scholar 

  5. Burt, P.J., and Adelson, E.H.: ‘The Laplacian Pyramid as a Compact Image Code’, IEEE Trans. Commun. 9, no. 4 (1983), 532–540.

    Google Scholar 

  6. Florack, L.M.J.: Image structure, Kluwer Acad. Publ., 1997.

    Google Scholar 

  7. Haar Romeny, B.Mter (ed.): Geometry-driven diffusion in computer vision, Kluwer Acad. Publ., 1994.

    MATH  Google Scholar 

  8. Haar Romeny, B. Mter, et al.: Proc. First Internat. Conf. scale-space, Vol. 1252 of Lecture Notes Computer Science, Springer, 1997.

    Google Scholar 

  9. Koenderink, J.J.: ‘The structure of images’, Biological Cybernetics 50 (1984), 363–370.

    MathSciNet  MATH  Google Scholar 

  10. Lindeberg, T.: Scale-space theory in computer vision, Kluwer Acad. Publ., 1994.

    Google Scholar 

  11. Sporring, J., et al.: Gaussian scale-space theory, Kluwer Acad. Publ., 1997.

    MATH  Google Scholar 

  12. Witkin, A.P.: ‘Scale-space filtering’: Proc. 8th Internat. Joint Conf. Art. Intell. Karlsruhe, West Germany Aug. 1983, 1983, pp. 1019–1022.

    Google Scholar 

  13. Young, R.A.: ‘The Gaussian derivative model for spatial vision: Retinal mechanisms’, Spatial Vision 2 (1987), 273–293.

    Google Scholar 

  14. Ahlfors, L.V.: Complex analysis, McGraw-Hill, 1953, p. 172.

    MATH  Google Scholar 

  15. Markushevich, A.I.: Theory of functions of a complex variable, Vol. II, Chelsea, 1977, p. Chap. 4. (Translated from the Russian.)

    MATH  Google Scholar 

  16. Frobenius, F.G.: ‘Über die Charactere der symmetrischen Gruppe’, Sitz. K. Preuss. Akad. Wiss (1900), 516–534, Also: Gesammelte Abh. 3 Springer, 1968, 148–166.

    Google Scholar 

  17. Jacobi, C.: ‘De functionibus alternantibus earumque divi-sione per productum e differentiis elementorum conflatum’, J. Reine Angew. Math. 22 (1841), 360–371, Also: Math. Werke 3, Chelsea, 1969, 439–452.

    MATH  Google Scholar 

  18. James, G.D., and Kerber, A.: The representation theory of the symmetric group, Vol. 16 of Encycl. Math. Appl., Addison-Wesley, 1981.

    MATH  Google Scholar 

  19. Knuth, D.E.: ‘Permutations, matrices and generalized Young tableaux’, Pacific J. Math. 34 (1970), 709–727.

    MathSciNet  MATH  Google Scholar 

  20. Kostka, C.: ‘Über den Zusammenhang zwischen einigen Formen von symmetrischen Funktionen’, Crelle’s J. 93 (1882), 89–123.

    MATH  Google Scholar 

  21. Littlewood, D.E.: The theory of group characters, Oxford Univ. Press, 1950.

    MATH  Google Scholar 

  22. Littlewood, D.E., and Richardson, A.R.: ‘Group characters and algebra’, Philos. Trans. R. Soc. London Ser. A 233 (1934), 99–142.

    Google Scholar 

  23. Macdonald, I.G.: Symmetric functions and Hall polynomials, second ed., Oxford Univ. Press, 1995.

    MATH  Google Scholar 

  24. Sagan, B.E.: The symmetric group: representations, combinatorial algorithms, and symmetric functions, Wadsworth&Brooks/Cole, 1991, Second ed.: Springer, to appear.

    MATH  Google Scholar 

  25. Schensted, C.: ‘Longest increasing and decreasing subsequences’, Canad. J. Math. 13 (1961), 179–191.

    MathSciNet  MATH  Google Scholar 

  26. Schur, I.: ‘Über eine Klasse von Matrizen die sich einer gegeben Matrix zuordnen lassen’, Inaugural Diss. Berlin (1901).

    Google Scholar 

  27. Trudi, N.: ‘Intorno un determinante piu generale di quello che suol dirsi determinante delle radici di una equazione, ed alle funzioni simmetriche complete di queste radici’, Rend. Accad. Sci. Fis. Mat. Napoli 3 (1864), 121–134, Also: Gior-nale di Mat. 2 (1864), 152–158; 180–186.

    Google Scholar 

  28. Akhiezer, N.I.: The classical moment problem, Hafner, 1965.

    MATH  Google Scholar 

  29. Alpay, D., Dijksma, A., Rovnyak, J., and Snoo, H.S.V. De: ‘Reproducing kernel Pontryagin spaces’: Holo-morphic spaces (Berkeley, CA, 1995), Cambridge Univ. Press, 1998, pp. 425–444.

    Google Scholar 

  30. Ball, J.A., Gohberg, I., and Rodman, L.: Interpolation of rational matrix functions, Vol. 45 of Oper. Th. Adv. Appi, Birkhäuser, 1990.

    MATH  Google Scholar 

  31. Branges, L. de, and Rovnyak, J.: Square summable power series, Holt, Rinehart&Winston, 1966.

    MATH  Google Scholar 

  32. Duren, P.L.: Theory of H P spaces, Acad. Press, 1970.

    MATH  Google Scholar 

  33. Dym, H.: ‘The commutant lifting approach to interpolation problems, by Ciprian Foias and Arthur E. Frazho (book review)’, Bull. Amer. Math. Soc. 31 (1994), 125–140.

    MathSciNet  Google Scholar 

  34. Foias, C., Frazho, A.E., Gohberg, I., and Kaashoek, M. A.: Metric constrained interpolation, commutant lifting and systems, Vol. 100 of Oper. Th. Adv. Appi, Birkhäuser, 1998.

    MATH  Google Scholar 

  35. Kailath, T.: ‘A theorem of I. Schur and its impact on modern signal processing’: I. Schur methods in operator theory and signal processing, Vol. 18 of Oper. Th. Adv. Appi, Birkhäuser, 1986, pp. 9–30.

    Google Scholar 

  36. Krein, M.G., and Langer, H.: ‘Über einige Fortsetzungsprobleme, die eng mit der Theorie hermitescher Operatoren im Raume II K zusammenhängen. I. Einige Funktionenklassen und ihre Darstellungen’, Math. Nachr. 77 (1977), 187–236.

    MathSciNet  MATH  Google Scholar 

  37. Nikolski, N., and Vasyunin, V.: ‘Elements of spectral theory in terms of the free function model. I. Basic constructions’: Holomorphic spaces (Berkeley, CA, 1995), Cambridge Univ. Press, 1998, pp. 211–302.

    Google Scholar 

  38. Potapov, V.P.: Collected papers, Hokkaido Univ. Research Inst. Applied Electricity, Division Appl. Math., Sapporo, 1982, Edited and transl. by T. Ando.

    Google Scholar 

  39. Sakhnovich, L.A.: Interpolation theory and its applications, Kluwer Acad. Publ., 1997.

    MATH  Google Scholar 

  40. Sarason, D.: ‘Generalized interpolation in H ’, Trans. Amer. Math. Soc. 127 (1967), 179–203.

    MathSciNet  MATH  Google Scholar 

  41. Sarason, D.: Sub-Hardy Hilbert spaces in the unit disk, Wiley, 1994.

    Google Scholar 

  42. Schur, I.: ‘Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind. I–II’, J. Reine Angew. Math. 147–148 (1917–1918), 205–232; 122–145, Also: Gesammelte Abh. II, no. 29–30. English transl.: I. Schur methods in operator theory and signal processing, Vol. 18 of Oper. Th. Adv. Appl., Birkhäuser, 1986, pp. 31–59; 61–88.

    Google Scholar 

  43. SzNagy, B., and Foias, C.: Harmonic analysis of operators on Hilbert space, North-Holland, 1970.

    Google Scholar 

  44. Chow, Y.S., Robbins, H., and Siegmund, D.: The theory of optimal stopping, Dover, reprint, 1991, Orignal: Houghton-Mifflin, 1971.

    MATH  Google Scholar 

  45. Freedman, P.R.: ‘The secretary problem and its extensions: a review’, Internat. Statist. Review 51 (1983), 189–206.

    Google Scholar 

  46. Birkhoff, G., and MacLane, S.: A survey of modern algebra, Macmillan, 1961.

    Google Scholar 

  47. Finkbeiner, D.T.: Introduction to matrices and linear transformations, Freeman, 1960.

    MATH  Google Scholar 

  48. Hall, G.S.: Differential geometry, Vol. 12 of Banach Centre Publ, Banach Centre, 1984, p. 53.

    Google Scholar 

  49. Hawking, S.W., and Ellis, G.F.R.: The large scale structure of space-time, Cambridge Univ. Press, 1973.

    MATH  Google Scholar 

  50. Kramer, D., Stephani, H., MacCallum, M.A.H., and Herlt, E.: Exact solutions of Einstein’s field equations, Cambridge Univ. Press, 1980.

    MATH  Google Scholar 

  51. Petrov, A.Z.: Einstein spaces, Pergamon, 1969.

    MATH  Google Scholar 

  52. Plebanski, J.F.: ‘The algebraic structure of the tensor of matter’, Acta Phys. Polon. 26 (1964), 963.

    MathSciNet  Google Scholar 

  53. Donaldson, S.K.: ‘The Seiberg-Witten equations and 4-manifold topology’, Bull. Amer. Math. Soc. 33 (1996), 45–70.

    MathSciNet  MATH  Google Scholar 

  54. Donaldson, S.K., and Kronheimer, P.B.: The geometry of four manifolds, Oxford Univ. Press, 1990.

    MATH  Google Scholar 

  55. Kronheimer, P.B., and Mrowka, T.S.: ‘The genus of embedded surfaces in the projective plane’, Math. Res. Lett. 1 (1994), 797–808.

    MathSciNet  MATH  Google Scholar 

  56. Kronheimer, P.B., and Mrowka, T.S.: ‘Recurrence relations and asymptotics for four manifold invariants’, Bull. Amer. Math. Soc. 30 (1994), 215–221.

    MathSciNet  MATH  Google Scholar 

  57. Seiberg, N., and Witten, E.: ‘Electric-magnetic duality, monopole condensation, and confinement in N = 2 supersym-metric Yang-Mills theory’, Nucl. Phys. B426 (1994), 19–52, Erratum: B430 (1994), 485–486.

    MathSciNet  Google Scholar 

  58. Seiberg, N., and Witten, E.: ‘Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD’, Nucl. Phys. B431 (1994), 484–550.

    MathSciNet  Google Scholar 

  59. Witten, E.: ‘Topological quantum field theory’, Comm. Math. Phys. 117 (1988), 353–386.

    MathSciNet  MATH  Google Scholar 

  60. Witten, E.: ‘Monopoles and four-manifolds’, Math. Res. Lett. 1 (1994), 769–796.

    MathSciNet  MATH  Google Scholar 

  61. Clancey, K.: Seminormal operators, Vol. 742 of Lecture Notes Math., Springer, 1979.

    MATH  Google Scholar 

  62. Conway, J.B.: Theory of subnormal operators, Vol. 36 of Math. Surveys Monogr., Amer. Math. Soc, 1991.

    MATH  Google Scholar 

  63. Gohberg, I., Goldberg, S., and Kaashoeck, M.A.: Classes of linear operators, Birkhäuser, 1990/3.

    MATH  Google Scholar 

  64. Helton, J.W., and Howe, R.: “Traces of commutators of integral operators’, Acta Math. 135 (1975), 271–305.

    MathSciNet  MATH  Google Scholar 

  65. Martin, M., and Putinar, M.: Lectures on hyponormal operators, Birkhäuser, 1989.

    MATH  Google Scholar 

  66. Pincus, J.D.: ‘Commutators and systems of singular integral equations I’, Acta Math. 121 (1968), 219–249.

    MathSciNet  MATH  Google Scholar 

  67. Xia, D.: Spectral theory of hyponormal operators, Birkhäuser, 1983.

    MATH  Google Scholar 

  68. Baire, R.: ‘Sur les fonctions des variables réelles’, Ann. Mat. Pura Appl. 3 (1899), 1–122.

    Google Scholar 

  69. Bouziad, A.: ‘Every Cech-analytic Baire semitopological group is a topological group’, Proc. Amer. Math. Soc. 124 (1996), 953–959.

    MathSciNet  MATH  Google Scholar 

  70. Cauchy, A.L.: Cours d’Analyse de l’Ecole Polytechnique, 1821.

    Google Scholar 

  71. Christensen, J.P.R.: ‘Joint continuity of separately continuous functions’, Proc. Amer. Math. Soc. 82 (1981), 455–462.

    MathSciNet  MATH  Google Scholar 

  72. Ellis, R.: ‘Locally compact transformation groups’, Duke Math. J. 24 (1957), 119–125.

    MathSciNet  MATH  Google Scholar 

  73. Ellis, R.: ‘A note on the continuity of the inverse’, Proc. Amer. Math. Soc. 8 (1957), 372–373.

    MathSciNet  MATH  Google Scholar 

  74. Hahn, H.: Reelle Funktionen, Akad. Verlag, 1932, pp. 325–338.

    Google Scholar 

  75. Kershner, R.: ‘The continuity of functions of many variables’, Trans. Amer. Math. Soc. 53 (1943), 83–100.

    MathSciNet  MATH  Google Scholar 

  76. Namioka,I.: ‘Separate and joint continuity’, Pacific J. Math. 51 (1974), 515–531.

    MathSciNet  MATH  Google Scholar 

  77. Piotrowski, Z.: ‘Separate and joint continuity’, Real Anal. Exch. 11 (1985–86), 293–322.

    MathSciNet  Google Scholar 

  78. Piotrowski, Z.: ‘The genesis of separate versus joint continuity’, Tatra Mtn. Math. Publ. 8 (1996), 113–126.

    MathSciNet  MATH  Google Scholar 

  79. Raymond, J. Saint: ‘Jeux topologiques et espaces de Namioka’, Proc. Amer. Math. Soc. 87 (1983), 499–504.

    MathSciNet  MATH  Google Scholar 

  80. Talagrand, M.: ‘Espaces de Baire et espaces de Namioka’, Math. Ann. 270 (1985), 159–164.

    MathSciNet  MATH  Google Scholar 

  81. Thomae, J.: Abriss einer Theorie der complexen Funktionen, second ed., Louis Nebert Verlag, 1873.

    Google Scholar 

  82. Buekenhout, F. (ed.): The Handbook of Incidence Geometry, Buildings and Foundations, Elsevier, 1995.

    Google Scholar 

  83. Cohen, A.M.: ‘On a theorem of Cooperstein’, European J. Combin. 4 (1983), 107–126.

    MathSciNet  MATH  Google Scholar 

  84. Beaty, M.G., and Dodson, M.M.: ‘Abstract harmonic analysis and the sampling theorem’, in J.R. Higgins and R.L. Stens (eds.): Sampling Theory in Fourier and Signal Analysis: Advanced Topics, Clarendon Press, 1999.

    Google Scholar 

  85. Brown Jr., J.L.: ‘On the error in reconstructing a non-bandlimited function by means of the bandpass sampling theorem’, J. Math. Anal. Appl. 18 (1967), 75–84.

    MathSciNet  MATH  Google Scholar 

  86. Butzer, P.L.: ‘A survey of the Whittaker-Shannon sampling theorem and some of its extensions’, J. Math. Research Exp. 3 (1983), 185–212.

    MathSciNet  Google Scholar 

  87. Butzer, P.L., and Hauss, M.: ‘Applications of sampling theory to combinatorial analysis, Stirling numbers, special functions and the Riemann zeta function’, in J.R. Higgins and R.L. Stens (eds.): Sampling Theory in Fourier and Signal Analysis: Advanced Topics, Clarendon Press, 1999.

    Google Scholar 

  88. Butzer, P.L., Higgins, J.R., and Stens, R.L.: ‘Sampling theory of signal analysis 1950–1995’, in J.P. Pier (ed.): Development of Mathematics 1950–2000, Birkhäuser, to appear.

    Google Scholar 

  89. Butzer, P.L., and Jansche, S.: ‘The exponential sampling theorem of signal analysis’, Atti Sem. Fis. Univ. Modena 46 (1998), 99–122, C. Bardaro and others (eds.): Conf. in Honour of C. Vinti (Perugia, Oct. 1996).

    MathSciNet  MATH  Google Scholar 

  90. Butzer, P.L., and Nasri-Roudsari, G.: ‘Kramer’s sampling theorem in signal analysis and its role in mathematics’, in J.M. Blackedge (ed.): Image Processing: Math. Methods and Appl., Vol. 61 of Inst. Math. Appl. New Ser., Clarendon Press, 1997, pp. 49–95.

    Google Scholar 

  91. Butzer, P.L., Splettstösser, W., and Stens, R.L.: ‘The sampling theorem and linera predeiction in signal analysis’, Jahresber. Deutsch. Math. Ver. 90 (1988), 1–70.

    MATH  Google Scholar 

  92. Higgins, J.R.: ‘Five short stories about the cardinal series’, Bull. Amer. Math. Soc. 12 (1985), 45–89.

    MathSciNet  MATH  Google Scholar 

  93. Higgins, J.R.: Sampling theory in Fourier and signal analysis: Foundations, Clarendon Press, 1996.

    MATH  Google Scholar 

  94. Higgins, J.R., and Stens, R.L. (eds.): Sampling theory in Fourier and signal analysis: Advanced topics, Clarendon Press, 1999.

    MATH  Google Scholar 

  95. Jerri, A.J.: ‘The Shannon sampling theorem: its various extensions and applications: A tutorial review’, Proc. IEEE 65 (1977), 1565–1589.

    MATH  Google Scholar 

  96. Sloane, N.J.A., and Wyer, A.D. (eds.): Claude Elwood Shannon: Collected papers, IEEE, 1993.

    Google Scholar 

  97. Terras, A.: Harmonic analysis on symmetric spaces and applications, Vol. 1, Springer, 1985.

    MATH  Google Scholar 

  98. Zayed, A.I.: Advances in Shannon’s sampling theory, CRC, 1993.

    MATH  Google Scholar 

  99. Boardman, J.M., and Vogt, R.M.: Homotopy invariant algebraic structures on topological spaces, Vol. 347 of Lecture Notes Math., Springer, 1973.

    MATH  Google Scholar 

  100. Borsuk, K.: ‘Concerninghomotopy properties of compacta’, Fund. Math. 62 (1968), 223–254.

    MathSciNet  MATH  Google Scholar 

  101. Chapman, T.A.: ‘On some applications of infinite-dimensional manifolds to the theory of shape’, Fund. Math. 76 (1972), 181–193.

    MathSciNet  MATH  Google Scholar 

  102. Dydak, J.: ‘The Whitehead and the Smale theorems in shape theory’, Dissert. Math. 156 (1979), 1–55.

    MathSciNet  Google Scholar 

  103. Dydak, J., and Segal, J.: Shape theory: An introduction, Vol. 688 of Lecture Notes Math., Springer, 1978.

    MATH  Google Scholar 

  104. Edwards, D.A., and Hastings, H.M.: Cech and Steenrod homotopy theories with applications to geometric topology, Vol. 542 of Lecture Notes Math., Springer, 1976.

    MATH  Google Scholar 

  105. Fox, R.H.: ‘On shape’, Fund. Math. 74 (1972), 47–71.

    MathSciNet  MATH  Google Scholar 

  106. Grothendieck, A.: ‘Technique de descentes et théorèmes ‘existence en géométrie algébrique II’, Sém. Bourbaki 12 (1959/60), Exp. 190–195.

    Google Scholar 

  107. Günther, B., and Segal, J.: ‘Every attractor of a flow on a anifold has the shape of a finite polyhedron’, Proc. Amer. Math. Soc. 119 (1993), 321–329.

    MathSciNet  MATH  Google Scholar 

  108. Ivansic, I., Sher, R.B., and Venema, G.A.: ‘Complement theorems beyond the trivial range’, Illinois J. Math. 25 (1981), 209–220.

    MathSciNet  MATH  Google Scholar 

  109. Lisica, Ju.T., and Mardesic, S.: ‘Steenrod-Sitnikov homology for arbitrary spaces’, Bull. Amer. Math. Soc. 9 (1983), 207–210.

    MathSciNet  MATH  Google Scholar 

  110. Mardesic, S.: ‘On the Whitehead theorem in shape theory I’, Fund. Math. 91 (1976), 51–64.

    MathSciNet  MATH  Google Scholar 

  111. Mardesic, S.: ‘Strong expansions and strong shape theory’, Topology Appl. 38 (1991), 275–291.

    MathSciNet  MATH  Google Scholar 

  112. Mardesic, S., and Segal, J.: ‘Shapes of compacta and ANR-systems’, Fund. Math. 72 (1971), 41–59.

    MathSciNet  MATH  Google Scholar 

  113. Mardesic, S., and Segal, J.: Shape theory, North-Holland, 1982.

    MATH  Google Scholar 

  114. Morita, K.: ‘The Hurewicz and the Whitehead theorems in shape theory’, Reports Tokyo Kyoiku Daigaku Sec. A 12 (1974), 246–258.

    MATH  Google Scholar 

  115. Morita, K.: ‘On shapes of topological spaces’, Fund. Math. 86 (1975), 251–259.

    MathSciNet  MATH  Google Scholar 

  116. Breuil, C., Conrad, B., Diamond, F., and Taylor, R.: ‘Modularity of elliptic curves’, to appear.

    Google Scholar 

  117. Conrad, B., Diamond, F., and Taylor, R.: ‘Modularity of certain potentially Barsotti-Tate Galois representations’, J. Amer. Math. Soc. (to appear).

    Google Scholar 

  118. Diamond, F.: ‘On deformation rings and Hecke rings’, Ann. of Math. 144, no. 1–2 (1996), 137–166.

    MathSciNet  MATH  Google Scholar 

  119. Taylor, R., and Wiles, A.: ‘Ring-theoretic properties of certain Hecke algebras’, Ann. of Math. 141, no. 2–3 (1995), 553–572.

    MathSciNet  Google Scholar 

  120. Wiles, A.: ‘Modular elliptic curves and Fermat’s last theorem’, Ann. of Math. 141, no. 2–3 (1995), 443–551.

    MathSciNet  MATH  Google Scholar 

  121. Bredon, G.E.: Introduction to compact transformation groups, Acad. Press, 1972.

    MATH  Google Scholar 

  122. Gleason, A.M.: ‘Spaces with a compact Lie group of transformations’, Proc. Amer. Math. Soc. 1 (1950), 35–43.

    MathSciNet  MATH  Google Scholar 

  123. Hsiang, Wu Yl: Cohomology theory of topological transformation groups, Vol. 85 of Ergebn. Math., Springer, 1979.

    MATH  Google Scholar 

  124. Janich, K.: Differenzierbare G-Mannigfaltigkeiten, Vol. 6 of Lecture Notes Math., Springer, 1968.

    Google Scholar 

  125. Koszul, J.L.: ‘Sur certains groupes de transformation de Lie’, Colloq. Inst. C.N.R.S., Géom. Diff. 52 (1953), 137–142.

    MathSciNet  MATH  Google Scholar 

  126. Koszul, J.L.: Lectures on groups of transformations, Tata Inst., 1965.

    MATH  Google Scholar 

  127. Luna, D.: ‘Slices étales’, Bull. Soc. Math. France 33 (1973), 81–105.

    MATH  Google Scholar 

  128. Luna, D.: ‘Sur certaines opérations différentiates des groups de Lie’, Amer. J. Math. 97 (1975), 172–181.

    MathSciNet  MATH  Google Scholar 

  129. Montgomery, D., and Yang, C.T.: ‘The existence of slice’, Ann. of Math. 65 (1957), 108–116.

    MathSciNet  MATH  Google Scholar 

  130. Mostow, G.D.: ‘On a theorem of Montgomery’, Ann. of Math. 65 (1957), 432–446.

    MathSciNet  MATH  Google Scholar 

  131. Palais, R.: ‘Embeddings of compact differentiate transformation groups in orthogonal representations’, J. Math. Mech. 6 (1957), 673–678.

    MathSciNet  MATH  Google Scholar 

  132. Palais, R.S.: ‘Slices and equivariant imbeddings’: Sem. Transformation Groups, Princeton Univ. Press, 1960.

    Google Scholar 

  133. Popov, V.L., and Vinberg, E.B.: ‘Invariant theory’: Algebraic Geometry IV, Vol. 55 of Encycl. Math. Sci., Springer, 1994, pp. 122–284.

    Google Scholar 

  134. Delvos, F.-J., and Schempp, W.: Boolean methods in interpolation and approximation, Vol. 230 of Pitman Res. Notes Math., Longman, 1989.

    MATH  Google Scholar 

  135. Frank, K., Heinrich, S., and Pereverzev, S.: ‘Information complexity of multivariate Fredholm integral equations in Sobolev classes’, J. Complexity 12 (1996), 17–34.

    MathSciNet  MATH  Google Scholar 

  136. Genz, A.C.: ‘Fully symmetric interpolatory rules for multiple integrals’, SIAM J. Numer. Anal 23 (1986), 1273–1283.

    MathSciNet  MATH  Google Scholar 

  137. Griebel, M., Schneider, M., and Zenger, Ch.: ‘A combination technique for the solution of sparse grid problems’, in R. Beauwens and P. de Groen (eds.): Iterative Methods in Linear Algebra, Elsevier&North-Holland, 1992, pp. 263–281.

    Google Scholar 

  138. Novak, E., and Ritter, K.: ‘High dimensional integration of smooth functions over cubes’, Numer. Math. 75 (1996), 79–97.

    MathSciNet  MATH  Google Scholar 

  139. Smolyak, S.A.: ‘Quadrature and interpolation formulas for tensor products of certain classes of functions’, Soviet Math. Dokl. 4 (1963), 240–243.

    Google Scholar 

  140. Temlyakov, V.N.: Approximation of periodic functions, Nova Science, 1994.

    Google Scholar 

  141. Wasilkowski, G.W., and Wozniakowski, H.: ‘Explicit cost bounds of algorithms for multivariate tensor product problems’, J. Complexity 11 (1995), 1–56.

    MathSciNet  MATH  Google Scholar 

  142. Wasilkowski, G.W., and Wozniakowski, H.: ‘Weighted tensor-product algorithms for linear multivariate problems’, Preprint (1998).

    Google Scholar 

  143. Werschulz, A.G.: ‘The complexity of the Poisson problem for spaces of bounded mixed derivatives’, in J. Renegar, M. Shub, and S. Smale (eds.): The Mathematics of Numerical Analysis, Vol. 32 of Lect. Appl. Math., Amer. Math. Soc, 1996, pp. 895–914.

    Google Scholar 

  144. Arrow, K.J.: Social choice and individual values, seconded., Wiley, 1963.

    Google Scholar 

  145. Black, D.: The theory of committees and elections, Cambridge Univ. Press, 1958.

    MATH  Google Scholar 

  146. Borda, J.-Ch. de: ‘Mémoire sur les élections au scrutin’, Histoire Acad. R. des Sci. (1781).

    Google Scholar 

  147. Brams, S.J.: Rational politics: decisions, games, and strategy, CQ Press, 1985.

    Google Scholar 

  148. Brams, S.J., and Fishburn, P.C.: Approval voting, Birkhäuser, 1983.

    MATH  Google Scholar 

  149. Condorcet, Marquis de: Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix, Paris, 1785.

    Google Scholar 

  150. Farquarhson, R.: Theory of voting, Yale Univ. Press, 1969.

    Google Scholar 

  151. Fishburn, P.C.: The theory of social choice, Princeton Univ. Press, 1973.

    MATH  Google Scholar 

  152. Fishburn, P.C.: ‘Condorcet social choice functions’, SIAM J. Appl. Math. 33 (1977), 469–489.

    MathSciNet  MATH  Google Scholar 

  153. Fishburn, P.C.: Interprofile conditions and impossibility, Horwood, 1987.

    Google Scholar 

  154. Gehrlein, W.V.: ‘Condorcet’s paradox’, Theory and Decision 15 (1983), 161–197.

    MathSciNet  MATH  Google Scholar 

  155. Gibbard, A.: ‘Manipulation of voting schemes: a general result’, Econometrica 41 (1973), 587–601.

    MathSciNet  MATH  Google Scholar 

  156. Hare, T.: The election of representatives, parliamentary and municipal: a treatise, Longman, 1861.

    Google Scholar 

  157. Kelly, J.S.: Arrow impossibility theorems, Acad. Press, 1978.

    MATH  Google Scholar 

  158. May, K.O.: ‘A set of independent necessary and sufficient conditions for simple majority decisions’, Econometrica 20 (1952), 680–684.

    MATH  Google Scholar 

  159. Merrill, S.: Making multicandidate elections more democratic, Princeton Univ. Press, 1988.

    Google Scholar 

  160. Murakami, Y.: Logic and social choice, Routledge and Kegan Paul, 1968.

    Google Scholar 

  161. Peleg, B.: Game-theoretical analysis of voting in committees, Cambridge Univ. Press, 1984.

    Google Scholar 

  162. Saari, D.G.: Geometry of voting, Springer, 1994.

    MATH  Google Scholar 

  163. Satterthwaite, M.A.: ‘Strategy-proofness and Arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions’, J. Econom. Th. 10 (1975), 187–218.

    MathSciNet  MATH  Google Scholar 

  164. Young, H.P.: ‘Social choice scoring functions’, SIAM J. Appl. Math. 28 (1975), 824–838.

    MathSciNet  MATH  Google Scholar 

  165. Amemiya, I., and Araki, H.: ‘A remark on Piron’s paper’, Publ. Res. Inst. Math. Sci. A2 (1966/67), 423–427.

    MathSciNet  Google Scholar 

  166. Holland Jr., S.S.: ‘Orthomodularity in infinite dimensions: a theorem of M. Solèr’, Bull. Amer. Math. Soc. 32 (1995), 205–234.

    MathSciNet  MATH  Google Scholar 

  167. Keller, H.A.: ‘Ein nicht-klassischer Hilbertscher Raum’, Math. Z. 172 (1980), 41–49.

    MathSciNet  MATH  Google Scholar 

  168. Keller, H.A., Künzi, U.-M., and Wild, M. (eds.): Orthogonal geometry in infinite dimensional spaces, Vol. 53 of Bayreuth. Math. Schrift., 1998.

    Google Scholar 

  169. Piron, C.: ‘Axiomatique quantique’, Helv. Phys. Acta 37 (1964), 439–468.

    MathSciNet  MATH  Google Scholar 

  170. Prestel, A.: ‘On Solèr’s characterization of Hilbert spaces’, Manuscrita Math. 86 (1995), 225–238.

    MathSciNet  MATH  Google Scholar 

  171. Soler, M.P.: ‘Characterization of Hilbert spaces with ortho-modular spaces’, Commun. Algebra 23 (1995), 219–243.

    MathSciNet  MATH  Google Scholar 

  172. Wilbur, W. John: ‘On characterizing the standard quantum logics’, Trans. Amer. Math. Soc. 233 (1977), 265–292.

    MathSciNet  MATH  Google Scholar 

  173. Green, J.A.: Polynomial representations of GL n , Vol. 830 of Lecture Notes Math., Springer, 1980.

    MATH  Google Scholar 

  174. James, G.D.: The representation theory of the symmetric groups, Vol. 682 of Lecture Notes Math., Springer, 1978.

    MATH  Google Scholar 

  175. James, G.D., and Kerber, A.: The representation theory of the symmetric group, Vol. 16 of Encycl. Math. Appl., Addison-Wesley, 1981.

    MATH  Google Scholar 

  176. Mathieu, O.: ‘On the dimension of some modular irreducible representations of the symmetric group’, Lett. Math. Phys. 38 (1996), 23–32.

    MathSciNet  MATH  Google Scholar 

  177. Specht, W.: ‘Die irreduziblen Darstellungen der symmetrischen Gruppe’, Math. Z. 39 (1935), 696–711.

    MathSciNet  Google Scholar 

  178. Bérard, P.H.: Spectral geometry: Direct and inverse problems, Vol. 1207 of Lecture Notes Math., Springer, 1986.

    Google Scholar 

  179. Bérard, P.H.: ‘Variétés Riemanniennes isospectrales non isométriques’, Astérisque 177–178 (1989), 127–154.

    Google Scholar 

  180. Berger, M., Gauduchon, P., and Mazet, E.: Le spectre d’une variété Riemannienne, Vol. 194 of Lecture Notes Math., Springer, 1971.

    MATH  Google Scholar 

  181. Buser, P.: Geometry and spectra of compact Riemann surfaces, Vol. 106 of Progr. Math., Birkhäuser, 1992.

    MATH  Google Scholar 

  182. Cartier, P., and Voros, A.: ‘Une nouvelle interprétation de la formule des traces de Selberg’: The Grothendieck Festschrift: II, Vol. 87 of Progr. Math., Birkhäuser, 1990, pp. 1–67.

    MathSciNet  Google Scholar 

  183. Chavel, I.: Eigenvalues in Riemannian geometry, Acad. Press, 1984.

    MATH  Google Scholar 

  184. Gilkey, P.B.: ‘Spectral geometry of Riemannian manifolds’, Contemp. Math. 101 (1989), 147–153.

    MathSciNet  Google Scholar 

  185. Gilkey, P.B.: Invariance theory, the heat equation, and the Atiyah-Singer index theorem, 2nd ed., CRC, 1995.

    MATH  Google Scholar 

  186. Gordon, C.S.: ‘You can’t hear the shape of a manifold’: New Developments in Lie Theory and Their Applications. Proc. 3rd Workshop Represent. Th. Lie Groups Appl. (Cordoba, 1989), Vol. 105 of Progr. Math., Birkhäuser, 1992, pp. 129–146.

    Google Scholar 

  187. Gordon, C.S.: ‘Isospectral closed Riemannian manifolds which are not locally isometric I’, J. Diff. Geom. 37 (1993), 639–649.

    MATH  Google Scholar 

  188. Gordon, C.S.: ‘Isospectral closed Riemannian manifolds which are not locally isometric II’, Contemp. Math. 173 (1994), 121–131.

    Google Scholar 

  189. Gordon, C.S., Webb, D.L., and Wolpert, S.: ‘One can not hear the shape of a drum’, Bull. Amer. Math. Soc. 27, no. 1 (1992), 134–138.

    MathSciNet  MATH  Google Scholar 

  190. Kac, M.: ‘Can one hear the shape of a drum?’, Amer. Math. Monthly 73 (1966), 1–23.

    MATH  Google Scholar 

  191. McKean, H.P., and Singer, I.M.: ‘Curvature and the eigenvalues of the Laplacian’, J. Diff. Geom. 1 (1967), 43–69.

    MathSciNet  MATH  Google Scholar 

  192. Müller, W.: ‘Spectral theory and geometry’: First European Congress of Mathematics (Paris, July 6–10, 1992), Vol. I, Birkhäuser, 1994, pp. 153–185.

    Google Scholar 

  193. Osgood, B., Phillips, R., and Sarnak, P.: ‘Compact isospectral sets of surfaces’, J. Funct. Anal. 80 (1988), 212–234.

    MathSciNet  MATH  Google Scholar 

  194. Osgood, B., Phillips, R., and Sarnak, P.: ‘Extremals of determinants of Laplacians’, J. Funct. Anal. 80 (1988), 148–211.

    MathSciNet  MATH  Google Scholar 

  195. Osgood, B., Phillips, R., and Sarnak, P.: ‘Moduli spaces, heights and isospectral sets of plain domains’, Ann. of Math. 129 (1989), 293–362.

    MathSciNet  MATH  Google Scholar 

  196. Pesce, H.: ‘Variétés isospectrales et représentations de groupes’, Contemp. Math. 173 (1994), 231–240.

    MathSciNet  Google Scholar 

  197. Pesce, H.: ‘Représentations relativement équivalentes et variétés Riemanniennes isospectrales’, Comment. Math. Helvetici 71 (1996), 243–268.

    MathSciNet  MATH  Google Scholar 

  198. Pesce, H.: ‘Une réciproque générique du théorème de Sunada’, Compositio Math. 109 (1997), 357–365.

    MathSciNet  MATH  Google Scholar 

  199. Sunada, T.: ‘Riemannian coverings and isospectral manifolds’, Ann. of Math. 121 (1985), 169–186.

    MathSciNet  MATH  Google Scholar 

  200. VignÉras, M.F.: ‘Variétés Riemanniennes isospectrales et non isométriques’, Ann. of Math. 112 (1980), 21–32.

    MathSciNet  MATH  Google Scholar 

  201. Berard Bergery, L., and Bourguignon, J.P.: ‘Laplacians and Riemannian submersions with totally geodesic fibers’, Illinois J. Math. 26 (1982), 181–200.

    MathSciNet  MATH  Google Scholar 

  202. Gilkey, P., Leahy, J., and Park, J.H.: Spinors, spectral geometry, and Riemannian submersions, Vol. 40 of Lecture Notes, Research Inst. Math., Global Analysis Research Center, Seoul Nat. Univ., 1998.

    MATH  Google Scholar 

  203. Gilkey, P., Leahy, J., and Park, J.H.: ‘The eigenforms of the complex Laplacian for a holomorphic Hermitian submersion’, Nagoya Math. J. (to appear).

    Google Scholar 

  204. Gilkey, P., and Park, J.H.: ‘Riemannian submersions which preserve the eigenforms of the Laplacian’, Illinois J. Math. 40 (1996), 194–201.

    MathSciNet  MATH  Google Scholar 

  205. Goldberg, S.I., and Ishihara, T.: ‘Riemannian submersions commuting with the Laplacian’, J. Diff. Geom. 13 (1978), 139–144.

    MathSciNet  MATH  Google Scholar 

  206. Moroianu, A.: ‘Opérateur de Dirac et Submersions Riemanniennes’, Thesis Ecole Polytechn. Palaiseau (1996).

    Google Scholar 

  207. Muto, Y.: ‘δ commuting mappings and Betti numbers’, Tôhoku Math. J. 27 (1975), 135–152.

    Google Scholar 

  208. Muto, Y.: ‘Riemannian submersion and the Laplace-Beltrami operator’, Kodai Math. J. 1 (1978), 329–338.

    MathSciNet  MATH  Google Scholar 

  209. Muto, Y.: ‘Some eigenforms of the Laplace-Beltrami operators in a Riemannian submersion’, J. Korean Math. Soc. 15 (1978), 39–57.

    MathSciNet  MATH  Google Scholar 

  210. Watson, B.: ‘Manifold maps commuting with the Laplacian’, J. Diff. Geom. 8 (1973), 85–94.

    MATH  Google Scholar 

  211. Dawid, A.P.: ‘Spherical matrix distributions and multivariate model’, J. R. Statist. Soc. Ser. B 39 (1977), 254–261.

    MathSciNet  MATH  Google Scholar 

  212. Fang, K.T., and Zhang, Y.T.: Generalized multivariate analysis, Springer, 1990.

    MATH  Google Scholar 

  213. Gupta, A.K., and Varga, T.: Elliptically contoured models in statistics, Kluwer Acad. Publ., 1993.

    MATH  Google Scholar 

  214. Bauer, F.W.: ‘Extensions of generalized homology theories’, Pacific J. Math. 128, no. 1 (1987), 25–61.

    MathSciNet  MATH  Google Scholar 

  215. Eilenberg, S., and Steenrod, N.: Foundations of algebraic topology, Vol. 15 of Princeton Math. Ser., Princeton Univ. Press, 1952.

    Google Scholar 

  216. Milnor, J.: On the Steenrod homology theory, Berkeley, unpublished.

    Google Scholar 

  217. Sitnikov, K.: ‘Combinatorial topology of non-closed sets I’, Mat. Sb. 84, no. 76 (1954), 3–54. (In Russian.)

    MathSciNet  Google Scholar 

  218. Sitnikov, K.: ‘Combinatorial topology of non-closed sets I-II’, Mat. Sb. 37, no. 79 (1955), 355–434. (In Russian.)

    MathSciNet  Google Scholar 

  219. Steenrod, N.: ‘Regular cycles of compact metric spaces’, Amer. J. Math. 41 (1940), 833–85.

    MathSciNet  Google Scholar 

  220. Baillaud, B., and Bourget, H.: Correspondance d’Hermite et de Stieltjes, Vol. I, II, Gauthier-Villars, 1905.

    Google Scholar 

  221. Ehrich, S.: ‘Asymptotic properties of Stieltjes polynomials and Gauss-Kronrod quadrature formulae’, J. Approx. Th. 82 (1995), 287–303.

    MathSciNet  MATH  Google Scholar 

  222. Ehrich, S., and Mastroianni, G.: ‘Stieltjes polynomials and Lagrange interpolation’, Math. Comput. 66 (1997), 311–331.

    MathSciNet  MATH  Google Scholar 

  223. Gautschi, W., and Notaris, S.E.: ‘An algebraic study of Gauss-Kronrod quadrature formulae for Jacobi weight functions’, Math. Comput. 51 (1988), 231–248.

    MathSciNet  MATH  Google Scholar 

  224. Monegato, G.: ‘Stieltjes polynomials and related quadrature rules’, SIAM Review 24 (1982), 137–158.

    MathSciNet  MATH  Google Scholar 

  225. Notaris, S.E.: ‘Gauss-Kronrod quadrature for weight functions of Bernstein-Szegö type’, J. Comput. Appl. Math. 29 (1990), 161–169.

    MathSciNet  MATH  Google Scholar 

  226. Peherstorfer, F.: ‘Weight functions admitting repeated positive Kronrod quadrature’, BIT 30 (1990), 241–251.

    MathSciNet  Google Scholar 

  227. Peherstorfer, F.: ‘Stieltjes polynomials and functions of the second kind’, J. Comput. Appl. Math. 65 (1995), 319–338.

    MathSciNet  MATH  Google Scholar 

  228. Szegö, G.: ‘Über gewisse orthogonale Polynome, die zu einer oszillierenden Belegungsfunktion gehören’, Math. Ann. 110 (1934), 501–513, Collected papers, Vol.2, R. Askey (Ed.), Birkhäuser, 1982, 545–557.

    Google Scholar 

  229. Applebaum, D., and Hudson, R.L.: ‘Fermion diffusions’, J. Math. Phys. 25 (1984), 858–861.

    MathSciNet  Google Scholar 

  230. Asch, J., and Potthoff, J.: ‘A generalization of Itô’s lemma’, Proc. Japan Acad. 63A (1987), 289–291.

    MathSciNet  Google Scholar 

  231. Asch, J., and Potthoff, J.: ‘Itô’s lemma without non-anticipatory conditions’, Probab. Th. Rel. Fields 88 (1991), 17–46.

    MathSciNet  MATH  Google Scholar 

  232. Barnett, C., Streater, R.F., and Wilde, I.F.: ‘The Itô-Clifford integral’, J. Funct. Anal. 48 (1982), 172–212.

    MathSciNet  MATH  Google Scholar 

  233. Hida, T.: Brownian motion, Springer, 1980.

    MATH  Google Scholar 

  234. Hida, T., Kuo, H.-H., Potthoff, J., and Streit, L.: White noise: An infinite dimensional calculus, Kluwer Acad. Publ., 1993.

    MATH  Google Scholar 

  235. Kubo, I., and Takenaka, S.: ‘Calculus on Gaussian white noise, I–IV, Proc. Japan Acad. 56–58 (1980–1982), 376–380; 411–416; 433–437; 186–189.

    Google Scholar 

  236. Kuo, H.-H.: ‘Brownian functionals and applications’, Acta Applic. Math. 1 (1983), 175–188.

    MATH  Google Scholar 

  237. Kuo, H.-H., and Russek, A.: ‘White noise approach to stochastic integration’, J. Multivariate Anal. 24 (1988), 218–236.

    MathSciNet  MATH  Google Scholar 

  238. Nualart, D., and Pardoux, E.: ‘Stochastic calculus with anticipating integrands’, Th. Rel. Fields 78 (1988), 535–581.

    MathSciNet  MATH  Google Scholar 

  239. Potthoff, J.: ‘Stochastic integration in Hida’s white noise calculus’, in S. Albeverio and D. Merlini (eds.): Stochastic Processes, Physics and Geometry, 1988.

    Google Scholar 

  240. Russo, F., and Vallois, P.: ‘Forward, backward and symmetric stochastic integration’, Probab. Th. Rel. Fields 97 (1993), 403–421.

    MathSciNet  MATH  Google Scholar 

  241. Berntsen, J., and Espelid, T.O.: ‘On the use of Gauss quadrature in adaptive automatic integration schemes’, BIT 24 (1989), 239–242.

    MathSciNet  Google Scholar 

  242. Brass, H.: Quadraturverfahren, Vandenhoeck&Ruprecht, 1977.

    MATH  Google Scholar 

  243. Brass, H., and Hämmerlin, G. (eds.): Numerical integration IV, ISNM. Birkhäuser, 1994.

    Google Scholar 

  244. Davis, P.J., and Rabinowitz, P.: Methods of numerical integration, 2nd ed., Acad. Press, 1983.

    Google Scholar 

  245. Espelid, T.O., and Genz, A.: Numerical integration — Recent developments, software and applications, Vol. 357 of NATO ASI C: Math. Physical Sci., Kluwer Acad. Publ., 1992.

    Google Scholar 

  246. Favati, P., Lotti,G., and Romani, F.: Testing automatic quadrature programs, Calcolo, 1992, pp. 169–193.

    Google Scholar 

  247. Förster, K.-J.: ‘Über Monotonie und Fehlerkontrolle bei den Gregoryschen Quadraturverfahren’, ZAMM 67 (1987), 257–266.

    MATH  Google Scholar 

  248. Förster, K.-J.: ‘A survey of stopping rules in quadrature based on Peano kernel methods’, Suppl. Rend. Circ. Mat. Palermo II 33 (1993), 311–330.

    Google Scholar 

  249. Keast, P., and Fairweather, G. (eds.): Numerical integration — Recent development, software and applications, Reidel, 1987.

    Google Scholar 

  250. Laurie, D.P.: ‘Stratified sequences of nested quadrature formulas’, Quaest. Math. 15 (1992), 365–384.

    MathSciNet  MATH  Google Scholar 

  251. Lyness, J.N.: ‘When not to use an automatic quadrature routine’, SIAM Review 25 (1983), 63–87.

    MathSciNet  MATH  Google Scholar 

  252. Lyness, J.N., and Kaganove, J.J.: ‘A technique for comparing automatic quadrature routines’, Comput. J. 20 (1977), 170–177.

    MATH  Google Scholar 

  253. Piessens, R., Kapenga, E. de Doncker, Überhuber, C.W., and Kahaner, D.K.: QUADPACK: a subroutine package for automatic integration, Vol. 1 of Ser. Comput. Math., Springer, 1982.

    Google Scholar 

  254. Bauer, F.W.: ‘A shape theory with singular homology’, Pacific J. Math. 62, no. 1 (1976), 25–65.

    Google Scholar 

  255. Bauer, F.W.: ‘Duality in manifolds’, Ann. Mat. Pura Appl. 4, no. 136 (1984), 241–302.

    Google Scholar 

  256. Bauer, F.W.: ‘A strong shape theory admitting an 5-dual’, Topol. Appl. 62 (1995), 207–232.

    MATH  Google Scholar 

  257. Cathey, F.W.: ‘Strong shape theory’: Proc. Dubrovnik, Vol. 870 of Lecture Notes Math., Springer, 1981, pp. 215–238.

    Google Scholar 

  258. Edwards, D.A., and Hastings, H.M.: Cech and Steenrod homotopy theory with applications to geometric topology, Vol. 542 of Lecture Notes Math., Springer, 1976.

    Google Scholar 

  259. Guenther, B.: ‘Use of semi-simplicial complexes in strong shape theory’, Glascow Math. 27, no. 47 (1992), 101–144.

    MATH  Google Scholar 

  260. Haxhibeqiri, Q., and Novak, S.: ‘Duality between stable strong shape morphisms and stable homotopy classes’, Glascow Math, (to appear).

    Google Scholar 

  261. Lima, E.: ‘The Spanier-Whitehead duality in two new categories’, Summa Brasil. Math. 4 (1959), 91–148.

    MathSciNet  Google Scholar 

  262. Banach, S.: Théoriè des opérations linéaires, Monogr. Mat. Warsaw, 1932.

    Google Scholar 

  263. Diestel, J., and Uhl, J.: Vector measures, Vol. 15 of Surveys, Amer. Math. Soc, 1977.

    MATH  Google Scholar 

  264. Filter, W., and Labuda, I.: ‘Essays on the Orlicz-Pettis theorem F, Real Anal. Exch. 16 (1990/91), 393–403.

    MathSciNet  Google Scholar 

  265. Kalton, N.: ‘The Orlicz-Pettis theorem’, Contemp. Math. 2 (1980).

    Google Scholar 

  266. Orlicz, W.: ‘Beiträge zur Theorie der Orthogonalent Wicklungen II’, Studia Math. 1 (1929), 241–255.

    Google Scholar 

  267. Pettis, B.J.: ‘On integration in vector spaces’, Trans. Amer. Math. Soc. 44 (1938), 277–304.

    MathSciNet  Google Scholar 

  268. Carlsson, G.: ‘Segal’s Burnside ring conjecture and related problems in topology’: Proc. Internat. Congress Math. (Berkeley, Calif. 1986), Vol. 1–2, Amer. Math. Soc, 1987, pp. 574–579.

    Google Scholar 

  269. Miller, H.: ‘The Sullivan conjecture and homotopical representation theory’: Proc. Internat. Congress Math. (Berkeley, Calif., 1986), Vol. 1–2, Amer. Math. Soc, 1987, pp. 580–589.

    Google Scholar 

  270. Félix, Y., and Halperin, S.: ‘Rational LS category and its applications’, Trans. Amer. Math. Soc. 273 (1982), 1–37.

    MathSciNet  MATH  Google Scholar 

  271. Félix, Y., Halperin, S., and Thomas, J.C.: Rational homotopy theory, in preparation.

    Google Scholar 

  272. Halperin,S.: ‘Finiteness in the minimal models of Sullivan’, Trans. Amer. Math. Soc. 230 (1977), 173–199.

    MathSciNet  MATH  Google Scholar 

  273. Halperin, S.: ‘Lectures on minimal models’, Mémoire de la SMF 9/10 (1983).

    Google Scholar 

  274. Quillen, D.: ‘Rational homotopy theory’, Ann. of Math. 90 (1969), 205–295.

    MathSciNet  MATH  Google Scholar 

  275. Sullivan, D.: ‘Infinitesimal computations in topology’, Publ. IHES 47 (1977), 269–331.

    MATH  Google Scholar 

  276. Félix, Y., and Halperin, S.: ‘Rational LS category and its applications’, Trans. Amer. Math. Soc. 273 (1982), 1–37.

    MathSciNet  MATH  Google Scholar 

  277. Félix, Y., Halperin, S., and Thomas, J.C.: Rational homotopy theory, in preparation.

    Google Scholar 

  278. Halperin, S.: ‘Finiteness in the minimal models of Sullivan’, Trans. Amer. Math. Soc. 230 (1977), 173–199.

    MathSciNet  MATH  Google Scholar 

  279. Halperin, S.: ‘Lectures on minimal models’, Mémoire de la SMF 9/10 (1983).

    Google Scholar 

  280. Quillen, D.: ‘Rational homotopy theory’, Ann. of Math. 90 (1969), 205–295.

    MathSciNet  MATH  Google Scholar 

  281. Sullivan, D.: ‘Infinitesimal computations in topology’, Publ. IHES 47 (1977), 269–331.

    MATH  Google Scholar 

  282. Berele, A., and Regev, A.: ‘Hook Young diagrams with applications to combinatorics and to representations of Lie superalgebras’, Adv. Math. 64, no. 2 (1987), 118–175.

    MathSciNet  MATH  Google Scholar 

  283. Berezin, F.A.: ‘The mathematical basis of supersymmetric field theories’, Soviet J. Nucl. Phys. 29 (1979), 857–866.

    MathSciNet  MATH  Google Scholar 

  284. Berezin, F.A., and Kats, G.I.: ‘Lie groups with noncommuting parameters’, Mat. Sb. USSR 11 (1970), 311–320.

    Google Scholar 

  285. Bernstein, J.: ‘Lectures on supersymmetry’, in P. Deligne, P. Etingof, D. Freed, L. Jeffrey, D. Kazhdan, D. Morrison, and E. Witten (eds.): Quantum Fields and Strings: A Course for Mathematicians, Amer. Math. Soc., to appear.

    Google Scholar 

  286. Cohen, M., and Westreich, S.: ‘From supersymmetry to quantum commutativity’, J. Algebra 168 (1994), 1–27.

    MathSciNet  MATH  Google Scholar 

  287. Corwin, L., Ne’eman, Y., and Sternberg, S.: ‘Graded Lie algebras in mathematics and physics’, Rev. Mod. Phys. 47 (1975), 573–604.

    MathSciNet  MATH  Google Scholar 

  288. Green, M.B., Schwarz, J.H., and Witten, E.: Superstring Theory, Mon. Math. Phys. Cambridge Univ. Press, 1987.

    MATH  Google Scholar 

  289. Kac, V.G.: ‘Lie superalgebras’, Adv. Math. 26 (1977), 8–96.

    MATH  Google Scholar 

  290. Kac, V.G.: ‘Classification of infinite-dimensional simple linearly compact Lie superalgebras’, Adv. Math. 139 (1998), 1–55.

    MathSciNet  MATH  Google Scholar 

  291. Kantor, I.: ‘On the concept of determinant in the supercase’, Commun. Algebra 22, no. 10 (1994), 3679–3739.

    MathSciNet  MATH  Google Scholar 

  292. Kostant, B.: ‘Graded manifolds, graded Lie theory and pre-quantization’: Differential Geom. Methods in Math. Phys. Proc. Symp. Bonn 1975, Vol. 570 of Lecture Notes Math., Springer, 1977, pp. 177–306.

    Google Scholar 

  293. Leites, D.A.: ‘Introduction to the theory of supermanifolds’, Russian Math. Surveys 35 (1980), 3–57.

    MathSciNet  MATH  Google Scholar 

  294. Majid, S.: Foundations of quantum group theory, Cambridge Univ. Press, 1995.

    MATH  Google Scholar 

  295. Manin, Yu.I.: Gauge field theory and complex geometry, Springer, 1984.

    Google Scholar 

  296. Milnor, J., and Moore, J.: ‘On the Structure of Hopf algebras’, Ann. of Math. 81 (1965), 211–264.

    MathSciNet  MATH  Google Scholar 

  297. Ogievetski, V.I., and Mezinchesku, L.: ‘Boson-fermion symmetries and superfields’, Soviet Phys. Uspekhi 18, no. 12 (1975), 960–981.

    Google Scholar 

  298. Seiberg, N., and Witten, E.: ‘Monopoles, duality, and chiral symmetry breaking in N = 2 supersymmetric QCD’, Nucl. Phys. B 431 (1994), 581–640.

    MathSciNet  Google Scholar 

  299. Shnider, S., and Wells Jr., R.O.: ‘Supermanifolds, Super Twist or Spaces and Super Yang-Mills Fields’: Sém. Math. Sup., Les Presses de l’Univ. Montréal, 1989.

    Google Scholar 

  300. Yetter, D.: ‘Quantum groups and representations of monoidal categories’, Math. Proc. Cambridge Philos. Soc. 108 (1990), 261–290.

    MathSciNet  MATH  Google Scholar 

  301. Beth, T., Jungnickel, D., and Lenz, H.: Design theory, 2nd ed., Cambridge Univ. Press, 1999.

    Google Scholar 

  302. Colbourn, C.J., and Dinitz, J.H.: The CRC Handbook of combinatorial designs, CRC, 1996.

    MATH  Google Scholar 

  303. Ionin, Y.J.: ‘Building symmetric designs with building sets’, Designs, Codes and Cryptography 17 (1999), 159–175.

    MathSciNet  MATH  Google Scholar 

  304. Kantor, W.M.: ‘2-transitive symmetric designs’, Graphs Combin. 1 (1985), 165–166.

    MathSciNet  MATH  Google Scholar 

  305. Lam, C.W.H., Thiel, L.H., and Swiercz, S.: ‘The nonexistence of finite projective planes of order 10’, Canad. J. Math. 41 (1989), 1117–1123.

    MathSciNet  MATH  Google Scholar 

  306. FlÖer, A.: ‘Morse theory for lagrangean intersections’, J. Diff. Geom. 28 (1988), 513–547.

    Google Scholar 

  307. Flöer, A.: ‘Symplectic fixed points and holomorphic spheres’, Comm. Math. Phys. 120 (1989).

    Google Scholar 

  308. Gromov, M.: ‘Pseudoholomorphic curves in symplectic manifolds’, Invent. Math. 82 (1985), 307–347.

    MathSciNet  MATH  Google Scholar 

  309. Liu, G., and Tian, G.: ‘Flöer homology and Arnold conjecture’, J. Diff. Geom. 49 (1998), 1–74.

    MathSciNet  MATH  Google Scholar 

  310. McDuff, D., and Salamon, D.: J-holomorphic curves and quantum cohomology, Vol. 6 of Univ. Lecture Ser., Amer. Math. Soc., 1995.

    Google Scholar 

  311. Salamon, D., and Zehnder, E.: ‘Morse theory for periodic solutions of Hamiltonian systems and Maslov index’, Commun. Pure Appl. Math. 45 (1992), 1303–1360.

    MathSciNet  MATH  Google Scholar 

  312. Benveniste, A., Métivier, M., and Priouret, P.: Adaptive algorithms and stochastic approximations, Springer, 1990.

    MATH  Google Scholar 

  313. Guo, L., and Ljung, L.: ‘Performance analysis of generali tracking algorithms.’, IEEE Trans. Automat. Control 40 (1995), 1388–1402.

    MathSciNet  MATH  Google Scholar 

  314. Hannan, E.J., and Deistler, M.: The statistical theory of linear systems, Wiley, 1988.

    MATH  Google Scholar 

  315. Kushner, H.J., and Clark, D.S.: Stochastic approximation methods for constrained and unconstrained systems, Springer, 1978.

    Google Scholar 

  316. Ljung, L.: System identification: Theory for the user, 2nd ed., Prentice-Hall, 1999.

    Google Scholar 

  317. Ljung, L., and Söderström, T.: Theory and practice of recursive identification, MIT, 1983.

    MATH  Google Scholar 

  318. Söderström, T., and Stoica, P.: System identification, Prentice-Hall, 1989.

    MATH  Google Scholar 

  319. Solo, V., and Kong, X.: Adaptive signal processing algorithms, Prentice-Hall, 1995.

    Google Scholar 

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© 2000 Kluwer Academic Publishers and Elliott H. Lieb for “Lieb-Thirring inequalities” and “Thomas-Fermi theory”

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Hazewinkel, M. (2000). S. In: Hazewinkel, M. (eds) Encyclopaedia of Mathematics. Encyclopaedia of Mathematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-1279-4_19

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  • DOI: https://doi.org/10.1007/978-94-015-1279-4_19

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