Properties of the resolvent of the Laplace operator on a two-dimensional sphere and a trace formula

Abstract

In the work we study the properties of the resolvent of the Laplace–Beltrami operator on a two-dimensional sphere $S^2$. We obtain the regularized trace formula for the Laplace-Beltrami operator perturbed by the operator of multiplication by a function in $W^1_2(S^2)$.