Abstract

In [6] obtained a formula for even the addition of spherical harmonics, which became the starting point for the derivation of the first regularized trace for the Laplace - Beltrami operator with potential on the projective plane. Thanks to her, managed to get around to find asymptotic formulas for the associated Legendre polynomials in the three parameters, which is an impossible task for a long time. The results obtained were the basis for the calculation of the perturbation theory corrections, followed by access to the formulas for regularized traces of elliptic differential operators. In this paper we consider the problem of summation of divergent series class. We propose a method for calculating the corrections of perturbation theory for a differential operator with potential on the real projective plane. The method is applicable, in particular, for summing series with factorial growth of members.

Keywords

Differential operators, spectral theory, regularized traces, perturbation theory, eigen values.