Pego theorem on compact groups

TL;DR

This paper extends the Pego theorem, which characterizes precompact subsets via Fourier transform, to the setting of compact groups, including non-abelian cases.

Contribution

It provides the first proof of the Pego theorem analogue for compact groups, broadening its applicability beyond Euclidean spaces.

Findings

Established the Pego theorem analogue for compact groups.

Included non-abelian compact groups in the analysis.

Enhanced understanding of Fourier analysis on compact groups.

Abstract

The Pego theorem characterizes the precompact subsets of the square-integrable functions on $\mathbb{R}^n$ via the Fourier transform. We prove the analogue of the Pego theorem on compact groups (not necessarily abelian).