On wavelet coorbit spaces associated to different dilation groups

2024/11/13 by Führ, Hartmut, van Velthoven, Jordy Timo, Voigtlaender, Felix · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2411.08416

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.

Cited by

• Classifying Wavelet Coorbit Spaces in Dimension 2

Related

• Coorbit spaces associated to integrably admissible dilation groups
• Classifying decomposition and wavelet coorbit spaces using coarse geometry
• Dilational Symmetries of Decomposition and Coorbit Spaces
• Coorbit spaces and wavelet coefficient decay over general dilation groups
• Wavelet Coorbit Spaces viewed as Decomposition Spaces