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abstract: 'This paper ist concerned with recent progress in the context of coorbit space theory. Based on a square integrable group representation, the coorbit theory provides new families of associated smoothness spaces, where the smoothness of a function is measured by the decay of the associated voice transform. Moreover, by discretizing the representation, atomic decompositions and Banach frames can be constructed. Usually, the whole machinery works well if the associated reproducing kernel is [*integrable*]{} with respect to a weighted Haar measure on the group. In recent studies, it has turned out that to some extent coorbit spaces can still be established if this condition is violated. In this paper, we clarify in which sense atomic decompositions and Banach frames for these generalized coorbit spaces can be obtained.'
address:
- 'FB12 Mathematik und Informatik, Philipps-Universität, Marburg, Hans-Meerwein Stra[ß]{}e, Lahnberge, 35032 Marburg, Germany'
- 'Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, Genova, Italy'
- 'Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, Genova, Italy'
- 'FB12 Mathematik und Informatik, Philipps-Universität, Marburg, Hans-Meerwein Stra[ß]{}e, Lahnberge, 35032 Marburg, Germany'
- 'Department of Mathematics, University of Kaiserslautern, Paul-Ehrlich-Str. 31, 67663 Kaiserslautern, Germany'
- 'Institute for Computational Mathematics in Science and Technology, 