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

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 $a(\Omega)$. Also we point out the relation of that operator and the spectral asymptotics of a Hankel operator with an anti-analytic symbol.
 MSC Classifications: 47B10 - Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20]