Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Y. ABE, A necessary condition for the existence of peak functions, Mem. Fac. Sci. Kyushu Univ. Ser. A 37 (1983), 1–8.
R.F. BASENER, Peak points, barriers and pseudoconvex boundary points, Proc. Am. Math. Soc 65 (1977), 89–92.
E. BEDFORD and J.E. FORNAESS, A construction of peak functions on weakly pseudoconvex domains, Ann. Math. II Ser. 107 (1978), 555–568.
E. BISHOP, A general Rudin-Carleson theorem, Proc. Am. Math. Soc. 13 (1962), 140–143.
T. BLOOM, C∞ peak functions for pseudoconvex domains of strict type, Duke Math. J. 45 (1978), 133–147.
J. BRUNA and J. M. ORTEGA, Interpolation by holomorphic functions smooth to the boundary in the unit ball, preprint.
D. BURNS and E.L. STOUT, Extending functions from submanifolds of the boundary, Duke Math. J. 43 (1976), 391–404.
L. CARLESON, Sets of uniqueness for functions regular in the unit circle, Acta Math. 87 (1952), 325–345.
J. del CASTILLO, On interpolation, peak and zero set on a weakly pseudoconvex domain, Proceedings of 7th Spanish-Portuguese Conference on Math, Part II, Publ. Sec. Mat. Univ. Autonoma Barcelona 21 (1980), 175–176.
D. CATLIN, Global regularity of the \(\bar \partial \)-Neumann problem, Complex Analysis of Several Variables, Proc. Symp. Pure Math. 41, Am. Math. Soc., Providence, 1984, pp. 39–49.
J. CHAUMAT and A.-M. CHOLLET, Ensembles pics pour A∞(D), Ann. Inst. Fourier (Grenoble) 29 (3) (1979), 171–200.
J. CHAUMAT and A.-M. CHOLLET, Caractér et propriétés des ensembles localement pics de A∞(D), Duke Math. J. 47 (1980), 763–787.
J. CHAUMAT and A.-M. CHOLLET, Ensembles pics pour A∞(D) non globalement inclus dans une variété intégrale, Math. Ann. 258 (1982), 243–252.
A.-M. CHOLLET, Ensembles de zéros à la frontière de fonctions analytiques dans des domaines strictement pseudo-convexes, Ann. Inst. Fourier (Grenoble) 26 (1) (1976), 51–80.
A.-M. Chollet, Ensembles de zéros, ensembles pics pour A(D) et A∞(D), Complex Analysis (Québec), Progress in Math. 4, Birkhaüser, Boston, 1980, pp. 57–66.
R.R. COIFMAN and G. WEISS, Analyse Harmonique Non-Commutative sur Certains Espaces Homogènes, Lect. Notes in Math. 242, Springer-Verlag, Berlin, 1971.
J. P. D'Angelo, Finite-type conditions for real hypersurfaces in Cn, preprint.
A.M. DAVIE and B.K. ØKSENDAL, Peak interpolation sets for some algebras of analytic functions, Pac. J. Math. 41 (1972), 81–87.
T. DUCHAMP and E.L. STOUT, Maximum modulus sets, Ann. Inst. Fourier (Grenoble) 31 (3) (1981), 37–69.
F. FORELLI, Measures orthogonal to polydisc algebras, J. Math. Mech 17 (1968), 1073–1086.
J.E. FORNAESS, Peak points on weakly pseudoconvex domains, Math. Ann. 227 (1977), 173–175.
J.E. FORNAESS and B.S. HENRIKSEN, Characterization of global peak sets for A∞(D), Math. Ann. 259 (1982), 125–130.
J.E. FORNAESS and S.G. KRANTZ, Continuously varying peaking functions, Pac. J. Math. 83 (1979), 341–347.
J.E. FORNAESS and A. NAGEL, The Mergelyan property for weakly pseudoconvex domains, Man. Math. 22 (1977), 199–208.
J.E. FORNAESS and N. ØVRELID, Finitely generated ideals in A(ω), Ann. Inst. Fourier (Grenoble) 33 (1983), 77–86.
I. GLICKSBERG, Recent Results in Function Algebras, Regional Conf. Series 11, Am. Math. Soc., Providence, 1972.
J. GLOBEVNIK, Peak sets for polydisc algebras, Mich. Math. J. 29 (1982), 221–227.
J. GLOBEVNIK, Norm preserving interpolation sets for polydisc algebras, Math. Proc. Cam. Philos. Soc. 91 (1982), 291–303.
M. HAKIM and N. SIBONY, Quelques conditions pour l'existence de fonctions pics dans des domaines pseudoconvexes, Duke Math. J. 44 (1977), 399–406.
M. HAKIM and N. SIBONY, Ensembles pics dans des domaines strictement pseudoconvexes, Duke Math. J. 45 (1978), 601–617.
G.M. HENKIN and A.E. TUMANOV, Interpolation submanifolds of pseudoconvex manifolds, Tr. Am. Math. Soc. 115 (1980), 59–69.
B.S. HENRIKSEN, A peak set of Hausdorff dimension 2n-1 for the algebra A(D) in the boundary of a domain D with C∞-boundary in Cn, Math. Ann. 259 (1982), 271–277.
A. IORDAN, Peak sets in weakly pseudoconvex domains, Math. Z. 188 (1985), 171–188.
A. IORDAN, Ensembles de module maximal dans des domaines pseudoconvexes, C. R. Acad. Sci. Paris Sér I 300 (1985), 655–656.
A. IORDAN, Peak sets in pseudoconvex doamins with the (NP) property, Math. Ann. 272 (1985), 231–236.
T. JIMBO, Peak sets on the boundary of a weakly pseudoconvex domains, Math. Jap. 29 (1984), 51–55.
J.-M. LABONDE, thesis, Université de Paris-Sud, Centre d'Orsay, 1985.
A. NAGEL, Smooth zero sets and interpolation sets for some algebras of holomorphic functions on strictly pseudoconvex domains, Duke Math. J. 43 (1976), 323–348.
A. NAGEL, Cauchy transforms of measures and a characterization of smooth peak interpolation sets for the ball algebra, Rocky Mt. J. Math. 9 (1979), 299–305.
A. NAGEL and W. RUDIN, Local boundary behavior of bounded holomorphic functions, Can. J. Math. 30 (1978), 583–592.
A. V. NOELL, Properties of peak sets in weakly pseudoconvex domains in ℂ2, Math. Z. 186 (1984), 99–116.
A. V. NOELL, Interpolation in weakly pseudoconvex domains in ℂ2, Math. Ann. 270 (1985), 339–348.
A. V. NOELL, Differentiable peak-interpolation on bounded domains with smooth boundary, Bull. Lond. Math. Soc. 17 (1985), 134–136.
A. V. NOELL, Peak points in boundaries not of finite type, Pac. J. Math. 123 (1986), 385–390.
W. RUDIN, Function Theory in Polydiscs, W. A. Benjamin, New York, 1969.
W. RUDIN, Peak-interpolation sets of class ℂ1, Pac. J. Math. 75 (1978), 267–279.
W. RUDIN, Holomorphic Lipschitz functions in balls, Comment. Math. Helv. 53 (1978), 143–147.
R. SAERENS, Interpolation manifolds, Ann. Sc. Norm. Sup. Pisa Cl. Sci. IV Ser. 11 (1984), 177–211.
R. SAERENS and E. L. STOUT, Differentiable interpolation on the polydisc, Complex Variables 2 (1984), 271–282.
E. M. STEIN, Singular integrals and estimates for the Cauchy-Riemann equations, Bull. Am. Math. Soc. 79 (1973), 440–445.
B. STENSØNES, Zero sets for A∞ functions, preprint.
E. L. STOUT, The Theory of Uniform Algebras, Tarrytown-on-Hudson, New York, 1971.
E. L. STOUT, The dimension of peak-interpolation sets, Proc. Am. Math. Soc. 86 (1982), 413–416.
B. A. TAYLOR and D.L. WILLIAMS, The peak sets of Am, Proc. Am. Math. Soc. 24 (1970), 604–605.
A. E. TUMANOV, A peak set for the disc algebra of metric dimension 2.5 in the three-dimensional unit sphere, Math. USSR Izv. 11 (1977), 353–359.
R. E. VALSKII, On measures orthogonal to analytic functions in ℂn, Soviet Math. Dokl. 12 (1971), 808–812.
N. T. VAROPOULOS, Ensembles pics et ensembles d'interpolation pour les algèbres uniformes, C. R. Acad. Sci. Paris Sér. A 272 (1971), 866–867.
J. VERDERA, A remark on zero and peak sets on weakly pseudoconvex domains, Bull. Lond. Math. Soc. 16 (1984), 411–412.
B. M. WEINSTOCK, Zero-sets of continuous holomorphic functions on the boundary of a strongly pseudoconvex domain, J. Lond. Math. Soc. 18 (1978), 484–488.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1987 Springer-Verlag
About this paper
Cite this paper
Saerens, R. (1987). Interpolation theory in Cn: A suryey. In: Krantz, S.G. (eds) Complex Analysis. Lecture Notes in Mathematics, vol 1268. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097302
Download citation
DOI: https://doi.org/10.1007/BFb0097302
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-18094-4
Online ISBN: 978-3-540-47752-5
eBook Packages: Springer Book Archive