An integral transform connecting spherical analysis on harmonic NA groups to that of odd dimensional real hyperbolic spaces

TL;DR

This paper introduces an integral transform linking spherical analysis on harmonic NA groups with that on odd-dimensional real hyperbolic spaces, also providing new identities for Gauss hypergeometric functions.

Contribution

It establishes a novel integral transform bridging two areas of harmonic analysis and derives new integral identities for hypergeometric functions.

Findings

Established an integral transform connecting the two analyses.

Derived new integral identities for Gauss hypergeometric functions.

Enhanced understanding of spherical analysis on different geometric structures.

Abstract

The main aim of the present paper is to establish an integral transform connecting spherical analysis on harmonic NA groups to that of odd dimensional real hyperbolic spaces. Moreover, certain interesting integral identities for the Gauss hypergeometric functions have also been given.