Some estimates of the remainder in the expressions for the eigenvalue asymptotics of some singular integral operators

Abstract

Some estimates are given for the remainder in the expressions for eigenvalue asymptotics of operators of the type of Riesz' potential and logarithmic potential. As a corollary an estimate is obtained of the spectral asymptotics of an operator playing a role in the thin airplane wing theory. The method is elementary and it is based on the properties of the singular values of compact operators.