Spectral properties of an operator of Riesz potential type and its product with the Bergman projection on a bounded domain

An exact asymptotic formula for the singular values of the product of an operator of Riesz potential type and the Bergman projection on a bounded domain is obtained. It is shown that these singular values determine the length of the boundary of the domain. It was known before that the spectrum of the operator of Riesz potential type determines the area of the domain.