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Sets of determination and kernels of certain associated operators

Part of: Spaces and algebras of analytic functions

Published online by Cambridge University Press:  30 April 2010

Arne Stray
Arne Stray
Affiliation:
Department of Mathematics, University of Bergen, Johannes Bruns Gate 12, 5008 Bergen, Norway ([email protected])
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Abstract

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Let m be a measure supported on a relatively closed subset X of the unit disc. If f is a bounded function on the unit circle, let fm denote the restriction to X of the harmonic extension of f to the unit disc. We characterize those m such that the pre-adjoint of the linear map f → fm has a non-trivial kernel.

Keywords

Dirichlet algebrasrational approximationunit disc

MSC classification

Secondary: 30H50: Algebras of analytic functions 30H05: Bounded analytic functions
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 2 , June 2010 , pp. 503 - 510
Copyright
Copyright © Edinburgh Mathematical Society 2010