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 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.
Cite this article
Louis R. Bragg, Transmutations and Ascent. Z. Anal. Anwend. 10 (1991), no. 2, pp. 123–148DOI 10.4171/ZAA/436