Boundary behavior in Hilbert spaces of vector-valued analytic functions

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Boundary behavior in Hilbert spaces of vector-valued analytic functions. / Carlsson, Marcus.

In: Journal of Functional Analysis, Vol. 247, No. 1, 2007, p. 169-201.

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TY - JOUR

T1 - Boundary behavior in Hilbert spaces of vector-valued analytic functions

AU - Carlsson, Marcus

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

KW - vector-valued analytic functions

KW - non-tangential limits

KW - index

KW - invariant

KW - subspaces

U2 - 10.1016/j.jfa.2007.02.006

DO - 10.1016/j.jfa.2007.02.006

M3 - Article

VL - 247

SP - 169

EP - 201

JO - Journal of Functional Analysis

T2 - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 1

ER -