Fredholm operators on abelian phase spaces

TL;DR

This paper investigates the properties of Fredholm operators on coorbit spaces over locally compact abelian phase spaces, introducing new techniques that combine band-dominated operator theory with quantum harmonic analysis.

Contribution

It presents novel results on compactness and Fredholm properties without requiring countability assumptions on the underlying groups.

Findings

Established new criteria for Fredholm operators on coorbit spaces.

Merged band-dominated operator theory with quantum harmonic analysis.

Extended previous results to more general locally compact abelian groups.

Abstract

We study compactness and the Fredholm property for linear operators on coorbit spaces over locally compact abelian phase spaces. In contrast to previous works, we do not impose any countability assumptions on the underlying groups. Our results are achieved by merging tools from the theory of band-dominated operators with methods of quantum harmonic analysis, thereby achieving new results in both areas.