Wiener Tauberian theorem for hypergeometric transforms

TL;DR

This paper establishes a Wiener Tauberian theorem analogue for hypergeometric transforms and applies it to derive a Furstenberg-type theorem for harmonic functions.

Contribution

It introduces a new Wiener Tauberian theorem analogue specifically for hypergeometric transforms, expanding the theoretical framework.

Findings

Proved Wiener Tauberian theorem analogue for hypergeometric transforms

Derived a Furstenberg theorem analogue for harmonic functions

Extended harmonic analysis techniques to hypergeometric settings

Abstract

We prove a genuine analogue of Wiener Tauberian theorem for hypergeometric transforms. As an application we prove analogue of Furstenberg theorem on Harmonic functions.