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Boundary behavior in Hilbert spaces of vector-valued analytic functions

Carlsson, Marcus LU (2007) In Journal of Functional Analysis 247(1). p.169-201
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.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
vector-valued analytic functions, non-tangential limits, index, invariant, subspaces
in
Journal of Functional Analysis
volume
247
issue
1
pages
169 - 201
publisher
Elsevier
external identifiers
  • wos:000246633000005
  • scopus:34247226564
ISSN
0022-1236
DOI
10.1016/j.jfa.2007.02.006
language
English
LU publication?
yes
id
ff9a2127-0c03-4a81-b930-babe664901fb (old id 659432)
date added to LUP
2016-04-01 16:41:24
date last changed
2022-01-28 21:28:31
@article{ff9a2127-0c03-4a81-b930-babe664901fb,
  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.}},
  author       = {{Carlsson, Marcus}},
  issn         = {{0022-1236}},
  keywords     = {{vector-valued analytic functions; non-tangential limits; index; invariant; subspaces}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{169--201}},
  publisher    = {{Elsevier}},
  series       = {{Journal of Functional Analysis}},
  title        = {{Boundary behavior in Hilbert spaces of vector-valued analytic functions}},
  url          = {{http://dx.doi.org/10.1016/j.jfa.2007.02.006}},
  doi          = {{10.1016/j.jfa.2007.02.006}},
  volume       = {{247}},
  year         = {{2007}},
}