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Zeitschrift für Analysis und ihre Anwendungen

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Volume 10, Issue 2, 1991, pp. 123–148
DOI: 10.4171/ZAA/436

Published online: 1991-06-30

Transmutations and Ascent

Louis R. Bragg[1]

(1) Oakland University, Rochester, USA

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.

Keywords: Transmutation, Laplace transform, ascent, kernel function, hypergeometric operators, quasi inner product, generating functions

Bragg Louis: Transmutations and Ascent. Z. Anal. Anwend. 10 (1991), 123-148. doi: 10.4171/ZAA/436