Published online by Cambridge University Press: 20 November 2018
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.