Analogous function theories for certain singular partial differential equations (Q1068273)

In a preceding paper [ibid. 13, 191-214 (1983; Zbl 0554.35012)] the authors used transmutation operators to establish analogous function theories for the heat, the wave, and the Laplace equations. They proved that, under these operators, correspondences exist between fundamental solutions, polynomial solutions, associated functions, generating functions, and expansion theorems including Fourier transform criteria. In the paper under review, the authors extend those methods in order to obtain such correspondences in the case of analogous function theories for the heat, the GASPT, and the Euler-Poisson-Darboux equations.