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Fredholm composition operators. (English) Zbl 0860.47020

Summary: Fredholm composition operators on a variety of Hilbert spaces of analytic functions on domains in \(\mathbb{C}^n\), \(N\geq 1\), are characterized.

MSC:

47B38 Linear operators on function spaces (general)
46E20 Hilbert spaces of continuous, differentiable or analytic functions
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References:

[1] Paul S. Bourdon, Fredholm multiplication and composition operators on the Hardy space, Integral Equations Operator Theory 13 (1990), no. 4, 607 – 610. · Zbl 0723.47024 · doi:10.1007/BF01210404
[2] Joseph A. Cima, A theorem on composition operators, Banach spaces of analytic functions (Proc. Pelczynski Conf., Kent State Univ., Kent, Ohio, 1976) Springer, Berlin, 1977, pp. 21 – 24. Lecture Notes in Math., Vol. 604.
[3] Joseph A. Cima, James Thomson, and Warren Wogen, On some properties of composition operators, Indiana Univ. Math. J. 24 (1974/75), 215 – 220. · Zbl 0276.47038 · doi:10.1512/iumj.1974.24.24018
[4] C. C. Cowen and B. D. MacCluer, Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, 1995. · Zbl 0873.47017
[5] Osamu Hatori, Fredholm composition operators on spaces of holomorphic functions, Integral Equations Operator Theory 18 (1994), no. 2, 202 – 210. · Zbl 0815.47039 · doi:10.1007/BF01192459
[6] M. Jovovic and B. D. MacCluer, Composition operators on Dirichlet spaces, preprint.
[7] Norberto Kerzman, Hölder and \?^{\?} estimates for solutions of \partial \?=\? in strongly pseudoconvex domains, Comm. Pure Appl. Math. 24 (1971), 301 – 379. · Zbl 0205.38702 · doi:10.1002/cpa.3160240303
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