A genuine analogue of Wiener Tauberian theorem for $ \mathrm {SL}(2, \R)$

TL;DR

This paper establishes a true analogue of the Wiener Tauberian theorem specifically for integrable functions on the group SL(2, R), extending classical harmonic analysis results to this non-abelian setting.

Contribution

It introduces a genuine Wiener Tauberian theorem for SL(2, R), filling a gap in harmonic analysis for non-abelian groups.

Findings

Proves a Wiener Tauberian theorem for SL(2, R)

Extends classical harmonic analysis to non-abelian groups

Provides foundational results for analysis on SL(2, R)

Abstract

We prove a genuine analogue of Wiener Tauberian theorem for integrable functions on $\mathrm {SL}(2, \R).$