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Boundary behavior in Hilbert spaces of vector-valued analytic functions

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Author

Summary, in English

In this paper we study the boundary behavior of functions in Hilbert spaces of vector-valued analytic functions on the unit disc D. More specifically, we give operator-theoretic conditions on M-z, where M-z, denotes the operator of multiplication by the identity function on ID, that imply that all functions in the space have non-tangential limits a.e., at least on some subset of the boundary. The main part of the article concerns the extension of a theorem by Aleman, Richter and Sundberg in [A. Aleman, S. Richter, C. Sundberg, Analytic contractions and non-tangential limits, Trans. Amer. Math. Soc. 359 (2007)] to the case of vector-valued functions. (C) 2007 Elsevier Inc. All rights reserved.

Publishing year

2007

Language

English

Pages

169-201

Publication/Series

Journal of Functional Analysis

Volume

247

Issue

1

Document type

Journal article

Publisher

Elsevier

Topic

  • Mathematics

Keywords

  • vector-valued analytic functions
  • non-tangential limits
  • index
  • invariant
  • subspaces

Status

Published

ISBN/ISSN/Other

  • ISSN: 0022-1236