On Wavelet Coorbit Spaces Associated to Different Dilation Groups

Journal of Fourier Analysis and Applications, vol. 30

Abstract

Abstract This paper develops methods based on coarse geometry for the comparison of wavelet coorbit spaces defined by different dilation groups, with emphasis on establishing a unified approach to both irreducible and reducible quasi-regular representations. We show that the use of reducible representations is essential to include a variety of examples, such as anisotropic Besov spaces defined by general expansive matrices, in a common framework. The obtained criteria yield, among others, a simple characterization of subgroups of a dilation group yielding the same coorbit spaces. They also allow to clarify which anisotropic Besov spaces have an alternative description as coorbit spaces associated to irreducible quasi-regular representations.

Authors 3

1. Hartmut Führ corresponding Aachen Lehrstuhl für Geometrie und Analysis

   RWTH Aachen University

   Affiliation as printed

   Lehrstuhl für Geometrie und Analysis, RWTH Aachen University, 52056, Aachen, Germany

2. Jordy Timo van Velthoven

   University of Vienna

   Affiliation as printed

   Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria

3. Felix Voigtlaender

   Catholic University of Eichstätt-Ingolstadt

   Affiliation as printed

   Mathematical Institute for Machine Learning and Data Science (MIDS), Catholic University of Eichstätt-Ingolstadt (KU), Auf der Schanz 49, 85049, Ingolstadt, Germany