Results
Title

A CLASS OF POSITIVE DEFINITE SPHERICAL FUNCTIONS ON THE EUCLIDEAN MOTION GROUPS.

Authors

EDEKE, U. E.; ARIYO, R. D.; DADA, O. C.

Abstract

Let G be the Euclidean motion group G = ℝ n ⋊ SO(n) realized as the semi-direct product of ℝ n and SO(n). Let K = SO(n) be a compact subgroup of G. The set of positive definite spherical functions on G is studied. Among other things, a result of Bochner which characterizes a K- bi-invariant positive definite spherical function in any locally compact group, is extended to the Gelfand pair (ℝ n ⋊ SO(n), SO(n) ).

Subjects

BOCHNER'S theorem; SPHERICAL functions; COMPACT groups

Publication

Global Journal of Pure & Applied Sciences, 2024, Vol 30, Issue 4, p551

ISSN

1118-0579

Publication type

Academic Journal

DOI

10.4314/gjpas.v30i4.13