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Spectral Properties of the Commutator of Bergman's Projection and the Operator of Multiplication by an Analytic Function

Published online by Cambridge University Press:  20 November 2018

Milutin R. Dostanić
Milutin R. Dostanić*
Affiliation:
Matematički Fakultet, Studentski trg 16, 11000 Beograd, Serbia e-mail: [email protected]
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Abstract

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It is shown that the singular values of the operator $aP\,-\,Pa$, where $P$ is Bergman's projection over a bounded domain $\Omega $ and $a$ is a function analytic on $\bar{\Omega }$, detect the length of the boundary of $a\left( \Omega \right)$. Also we point out the relation of that operator and the spectral asymptotics of a Hankel operator with an anti-analytic symbol.

Keywords

47B10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 56 , Issue 2 , 01 April 2004 , pp. 277 - 292
Copyright
Copyright © Canadian Mathematical Society 2004

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