Hochschule Neubrandenburg, University of Applied Sciences, Brodaer Str. 2, 17033 Neubrandenburg, Germany'
- 'Katholische Universität Eichstätt-Ingolstadt, Ostenstra[ß]{}e 26, 85072 Eichstätt, Germany'
author:
- Stephan Dahlke
- Filippo De Mari
- Ernesto De Vito
- Lukas Sawatzki
- Gabriele Steidl
- Gerd Teschke
- Felix Voigtlaender
title: 'On the Atomic Decomposition of Coorbit Spaces with Non-Integrable Kernel'
---

Introduction {#intro}
============

This paper is concerned with specific problems arising in the context of signal analysis. The overall goal in signal analysis is the efficient extraction of the relevant information one is interested in. For this, the signal—usually modeled as an element in a suitable function space—has to be processed, denoised, compressed, etc. The first step is always to decompose the signal into appropriate building blocks. This is performed by an associated transform, such as the wavelet transform, the Gabor transform or the shearlet transform, just to name a few. Which transform to choose clearly depends on the type of information one wants to extract from the signal. In recent years, it has turned out that group theory—in particular representation theory—acts as a common thread behind many transforms. Indeed, many transforms are related with square-integrable representations of certain locally compact groups. For 