Elliptic transmutation I

Abstract
Given and similar , modelled on radial Laplace-Beltrami operators (ρp = , in this paper we begin the study of transmutations which leads to elliptic equations Working with and transmutations Q m → −D 2 for m > −½ and −D 2 → for m < −½, we obtain a transmutation formulation and derivation of many results of generalized axially symmetric potential theory in the first case and in both cases generalized Hilbert transforms (different). Canonical generalizations are then automatic using general transmutation theory.

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