Asymptotics of the spectral function of an elliptic differential operator of second order

Abstract

In the work the Riesz means of the spectral function of a boundary-value problem for an elliptic differential operator of second order are studied for the case of a geodesically concave boundary. Asymptotic formulas for the Riesz means with an estimate of the remainder term that is uniform over the entire domain are obtained in terms of the formal asymptotics of Green's function of the problem considered. An explicit expression is obtained for the spectral function in a neighborhood of the diagonal from which there follows, in particular, a precise estimate of the remainder term in the Weyl formula.