Transmutations and Ascent

Abstract

We treat the method of ascent for partial differential equations by means of transmutations. We construct a kernel function for the radial generalized axially symmetric potential theory Dirichlet problem that involves $n$ radial variables. We also construct ascent type formulas for hypergeometric functions of operators and apply one of them to construct a solution of an ill posed Cauchy problem. Generating functions of special multivariable solution sets of partial differential equations are also considered.