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

[摘要] It is shown that the singular values of the operator $aP-Pa$, where $P$ isBergman's projection over a bounded domain $Omega$ and $a$ is a functionanalytic on $ar{Omega}$, detect the length of the boundary of $a(Omega)$.Also we point out the relation of that operator and the spectral asymptotics of a Hankel operator with an anti-analytic symbol.

[学科分类] 数学（综合）