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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
Abstract
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.
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- Copyright © Canadian Mathematical Society 2004
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