THE RADIAL PART OF AN INVARIANT DIFFERENTIAL OPERATOR ON THE EUCLIDEAN MOTION GROUPS

THE RADIAL PART OF AN INVARIANT DIFFERENTIAL OPERATOR

Abstract

Let G be the Euclidean motion group realised as the semi direct product of Rn and SO(n), that is, G =
R^n ⋊ SO(n). The pair (R^n ⋊ SO(n), SO(n)) is called the Gelfand pair. In this work, among other things,
spherical analysis on the pair is presented, including an explicit determination of spherical function for G.