On Spherical Distributions

Abstract

In this paper, we begin with the study of the hyperbolic spaces H G where ???? = ????(????. ????; ????) and ???? = ????(????; ????) × ????(???? − ????, ????; ????), ???? = ℝ, ℂ or ℍ denotes the set of real numbers, complex numbers and quaternions respectively. In the articles of J. Faraut [2] and M.T. Kosters and G. van Dijk [4], spherical distributions were derived following two different methods. The first method is to describe the behavior of spherical distributions making use of the Fourier transform of finite and infinite functions. The second is to express them asM'S where ????′:????′ → ????′(????) is a transpose map and S is a solution to the differential equation LS  a(t)S"b(t)S' and making use of the hypergeometric functions. Now we show that spherical distributions T can be obtained through a particular distribution S on ℝ by solving the equation . S LS   The technique of Methe̒ e’s [6] is instrumental for the context.