Boundary behavior in Hilbert spaces of vector-valued analytic functions
Författare
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.
Avdelning/ar
Publiceringsår
2007
Språk
Engelska
Sidor
169-201
Publikation/Tidskrift/Serie
Journal of Functional Analysis
Volym
247
Issue
1
Dokumenttyp
Artikel i tidskrift
Förlag
Elsevier
Ämne
- Mathematics
Nyckelord
- vector-valued analytic functions
- non-tangential limits
- index
- invariant
- subspaces
Status
Published
ISBN/ISSN/Övrigt
- ISSN: 0022-1236