Spectral density for the Schroedinger operator with magnetic field in the unit complex ball: solutions of evolutionary equations and applications to special functions

摘要

The Schwartz kernel of the spectral density for the Schrodinger operator with magnetic field in the n-dimensional complex ball is given. As applications, we compute the heat, resolvent and the wave kernels. Moreover, the resolvent and wave kernels are used to establish two new formulas for the Gauss-hypergeometric function.