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A Beurling Theorem for Generalized Hardy Spaces on a Multiply Connected Domain

Published online by Cambridge University Press:  20 November 2018

Yanni Chen
Affiliation:
School of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710119, China email: [email protected]
Don Hadwin
Affiliation:
Department of Mathematics, University of New Hampshire, Durham, NH 03824, USA email: [email protected], [email protected]
Zhe Liu
Affiliation:
Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA email: [email protected]
Eric Nordgren
Affiliation:
Department of Mathematics, University of New Hampshire, Durham, NH 03824, USA email: [email protected], [email protected]
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Abstract

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The object of this paper is to prove a version of the Beurling–Helson–Lowdenslager invariant subspace theorem for operators on certain Banach spaces of functions on a multiply connected domain in $\mathbb{C}$. The norms for these spaces are either the usual Lebesgue and Hardy space norms or certain continuous gauge norms. In the Hardy space case the expected corollaries include the characterization of the cyclic vectors as the outer functions in this context, a demonstration that the set of analytic multiplication operators is maximal abelian and reflexive, and a determination of the closed operators that commute with all analytic multiplication operators.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2018

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