In this paper exact asymptotic formulae are found for singular values of the Cauchyoperator and the logarithmic potential type operator (on a bounded domain), as well as their productswith Bergman's projection. It is shown that these spectral characteristics detect geometric propertiesof a domain $\Omega$ (area and the length of the boundary). The hypothesis “can we hear theshape of a drum”, from a paper by J.M. Anderson, D. Khavinson, and V. Lomonosov [‘Spectralpropertiesof some integral operators arising in potential theory’, {\em Quart.\ J. Math.\Oxford} (2) 43 (1992) 387-407], is correct in the above sense.

1991 Mathematics SubjectClassification: 47B10.