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Scattering theory, unitary dilations and Gaussian processes

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Three Decades of Mathematical System Theory

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 135))

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References

  1. Adamjan, V.M. and Arov, D.Z.: On unitary couplings of semi-unitary operators, Amer. Math. Soc. Transl. 95(2)(1970), 75–129.

    Google Scholar 

  2. Adamjan, V.M., Arov, D.Z., and Krein, M.G.: Infinite Hankel block matrices and related extension problems, Amer. Math. Soc. Transl. 3(2)(1978), 133–156.

    Google Scholar 

  3. Adamjan, V.M., Arov, D.Z., and Krein, M.G.: Infinite Hankel matrices and generalized Caratheodory-Fejer and Riesz problems, Functional Anal. Appl. 2. (1968), 1–18.

    Article  Google Scholar 

  4. Adamjan, V.M., Arov, D.Z., and Krein, M.G.: Analytic properties of Schmidt pairs for a Hankel operator and the generalized Schur-Takagi problem, Mat. Sb. 86(128(1971), 34–75; Math. U.S.S.R. Sb. (1971), 31–73.

    Google Scholar 

  5. Avniel, Y.: Realization and approximation of stationary stochastic processes, Report LIDS-TH-1440, Laboratory for Information and Decision System, MIT, Cambridge, MA., February 1985.

    Google Scholar 

  6. Ball, J. and Helton, W.: Interpolation problems of Pick-Nevanlinna and Loewner types for meromorphic matrix functions: parametrization of the set of all solutions, Integral Equations and Operator Theory, 9, 1986, 155–203.

    Article  Google Scholar 

  7. Bloomfield, P.B., Jewell, N.P., and Hayashi, E.: Characterizations of completely nondeterministic stochastic processes, Pacific J. of Math. 107 (1983), 307–317.

    Google Scholar 

  8. Davies, E.B.: Quantum Theory of Open Systems, Academic Press, New York, 1976.

    Google Scholar 

  9. Evans, D.E. and Lewis,J.T.: Dilations of irreversible evolutions in algebraic quantum theory, Comm. of Dublin Institute for Advanced Studies, No. 24, 1977.

    Google Scholar 

  10. Foias, C. and Frazho, E.: A note on unitary dilation theory and state spaces, Acta Sci. Math. 45 (1983), 165–175.

    Google Scholar 

  11. Ford, G.W., Kac, M., and Mazur, P.: Statistical mechanics of assemblies of coupled oscillators, J. of Math. Physics, 6, 1965, 504–515.

    Article  Google Scholar 

  12. Fuhrmann, P.A.: Linear Systems and Operators in Hilbert Space. McGraw-Hill, New York, 1981.

    Google Scholar 

  13. Glover, K.: All optimal Hankel-norm approximations of linear multi-variable systems and their L∞-error bounds, Int.J. of Control, 39, 1984, 1115–1193.

    Google Scholar 

  14. Helson, H.: Lectures on Invariant Subspaces. Academic Press, New York, 1964.

    Google Scholar 

  15. Lax, P.D. and Phillips, R.S.: Scattering Theory. Academic Press, New York, 1967.

    Google Scholar 

  16. Levinson, N. and McKean, H.P.: Weighted trigonometrical approximations on R′ with applications to the Germ field of stationary Gaussian Noise, Acta Math., 112, 1964, 99–143.

    Google Scholar 

  17. Lewis, J.T. and Thomas, L.C.: How to make a heat bath, Functional Integration, ed. A.M. Arthurs, Oxford, Clarendon Press 1974.

    Google Scholar 

  18. Lindquist, A. and Picci, G.: Realization theory for multivariate stationary Gaussian processes, SIAM J. Control and Optimization 23 (1985), 809–857.

    Article  Google Scholar 

  19. Sz-Nagy, B. and Foias, C.: Harmonic Analysis of Operators on Hilbert Space. Amsterdam, North-Holland, 1970.

    Google Scholar 

  20. Picci, G.: Application of Stochastic Realization Theory to a Fundamental Problem of Statistical Physics, in Modelling, Identification and Robust Control, (eds.: C.I. Byrnes and A. Lindquist), Elsevier Science Publishers B.V. (North-Holland), 1986.

    Google Scholar 

  21. Rozanov, Y.A.: Stationary Random Processes. Holden-Day, San Francisco, 1963.

    Google Scholar 

  22. Willems, J.C. and Heij, C.: Scattering Theory and Approximation of Linear Systems, in Proceedings of the 7th International Symposium on the Mathematical Theory of Networks and Systems MTNS-85, June 10–14, 1985, Stockholm, North-Holalnd, Amsterdam, 1985.

    Google Scholar 

  23. Willems, J.C.: Models for Dynamics, to appear in Dynamics Reported.

    Google Scholar 

  24. Zames, G.: Private Communication.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science and Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, 02139, Cambridge, MA, U.S.A.

    S. K. Mitter

  2. Scuola Normale Superiore, Pisa, Italy

    S. K. Mitter

  3. Department of Electrical and Computer Engineering, Drexel University, 19104, Philadelphia, PA, U.S.A.

    Y. B. Avniel

Authors
  1. S. K. Mitter
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  2. Y. B. Avniel
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Hendrik Nijmeijer Johannes M. Schumacher

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© 1989 Springer-Verlag

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Mitter, S.K., Avniel, Y.B. (1989). Scattering theory, unitary dilations and Gaussian processes. In: Nijmeijer, H., Schumacher, J.M. (eds) Three Decades of Mathematical System Theory. Lecture Notes in Control and Information Sciences, vol 135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0008467

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  • DOI: https://doi.org/10.1007/BFb0008467

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