Characterization of coorbit spaces with phase-space covers

TL;DR

This paper generalizes the characterization of coorbit spaces using phase-space covers, extending results from time-frequency analysis to include time-scale decompositions and irregular settings.

Contribution

It introduces a new framework for characterizing coorbit spaces with arbitrary phase-space covers, broadening the scope of analysis methods.

Findings

Coorbit spaces characterized by phase-space covers.

Extension of results from time-frequency to time-scale analysis.

Application to irregular phase-space decompositions.

Abstract

We show that coorbit spaces can be characterized in terms of arbitrary phase-space covers, which are families of phase-space multipliers associated with partitions of unity. This generalizes previously known results for time-frequency analysis to include time-scale decompositions. As a by-product, we extend the existing results for time-frequency analysis to an irregular setting.