Eigenvalue asymptotics for potential type operators on Lipschitz surfaces (Q871779)

The main result of the paper is the following theorem. Let \(A\) be a pseudodifferential operator in \(\mathbb R^{d+1}\) of order \(m-1,\) \(m<0,\) and let \(S\) be a compact Lipschitz surface in \(\mathbb R^{d+1}.\) Denote by \(\mathcal R\) the restriction of \(A\) on \(S\) and let \(f\) be a bounded measurable function on \(S\). Then the eigenvalues of the potential type operator \(f{\mathcal R}f\) satisfy the asymptotic formula \(\lim_{n\to \infty} \lambda_n^{\pm} n^{-m/d}= C^{\pm},\) where the coefficients \(C^{\pm}\) are given explicitly. The method is based on approximation of \(S\) by smooth surfaces.