Boundary behavior in Hilbert spaces of vector-valued analytic functions

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Bibtex

@article{ff9a21270c034a81b930babe664901fb,
title = "Boundary behavior in Hilbert spaces of vector-valued analytic functions",
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.",
keywords = "vector-valued analytic functions, non-tangential limits, index, invariant, subspaces",
author = "Marcus Carlsson",
year = "2007",
doi = "10.1016/j.jfa.2007.02.006",
language = "English",
volume = "247",
pages = "169--201",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Elsevier",
number = "1",

}