| Title | Boundary behavior in Hilbert spaces of vector-valued analytic functions |
| Authors | Marcus Carlsson |
| Alternative Location | http://dx.doi.org/10.1016/j..., Restricted Access |
| Publication | JOURNAL OF FUNCTIONAL ANALYSIS |
| Year | 2007 |
| Volume | 247 |
| Issue | 1 |
| Pages | 169 - 201 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| Abstract 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. |
| Keywords | vector-valued analytic functions, non-tangential limits, index, invariant, subspaces, |
| ISBN/ISSN/Other | ISSN: 0022-1236 |
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