Asymptotic expansions of traces for certain convolution operators

Abstract:

A version of Szegö’s theorem in Euclidean space gives the first two terms of the asymptotics as $\alpha \to \infty$ of the determinant of convolution operators on ${L_2}(\alpha \Omega )$, where $\Omega$ is a bounded subset of ${{\mathbf {R}}^n}$ with smooth boundary. In this paper the more general problem of the asymptotics of traces of certain analytic functions of the operators is considered and the next term in the expansion is obtained.