# The Paley-Wiener-Gelfand tauberian theorem for semigroups with invariant measure

## TL;DR

This paper extends the Paley-Wiener-Gelfand Tauberian theorem to abelian topological semigroups with invariant measure, broadening its applicability in harmonic analysis.

## Contribution

It generalizes the Gelfand version of the Paley-Wiener Tauberian theorem to a wider class of semigroups with invariant measures.

## Key findings

- The theorem is proved for abelian topological semigroups with invariant measure.
- Several corollaries of the generalized theorem are provided.

## Abstract

The theorem is proved that generalizes the Gelfand generalization of the Paley-Wiener tauberian theorem to general abelian topological semigroups with invariant measure. Several corollaries of this theorem are given.