Boundary behavior in Hilbert spaces of vector-valued analytic functions

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Abstract

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.
Original languageEnglish
Pages (from-to)169-201
JournalJournal of Functional Analysis
Volume247
Issue number1
DOIs
Publication statusPublished - 2007

Subject classification (UKÄ)

  • Mathematics

Keywords

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

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