Advanced

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
2007-12-05 15:39:41
date last changed
2017-01-01 07:12:18
@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},
  keyword      = {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},
  volume       = {247},
  year         = {2007},
}