Classifying Wavelet Coorbit Spaces in Dimension 2

2025/08/06 by Asharaf, Noufal, Führ, Hartmut, Jayaprakash, Vaishakh
#42C15 #42C40 #43A15 #FOS: Mathematics #Functional Analysis (math.FA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2508.04521

Abstract

Coorbit spaces provide a rigorous framework for the assessment of the approximation theoretic properties of generalized wavelet systems. It is therefore useful to understand when two different wavelet systems give rise to the same scales of coorbit spaces. This paper provides an exhaustive answer to this question for the case of continuous wavelet transforms associated with matrix groups in dimension two.

Citations

• On wavelet coorbit spaces associated to different dilation groups
• Dilational Symmetries of Decomposition and Coorbit Spaces
• Classifying decomposition and wavelet coorbit spaces using coarse geometry
• Coorbit spaces associated to integrably admissible dilation groups
• Wavelet Coorbit Spaces viewed as Decomposition Spaces
• Coorbit spaces and wavelet coefficient decay over general dilation groups
• Continuous characterizations of Besov-Lizorkin-Triebel spaces and new interpretations as coorbits
• Generalized Calderón conditions and regular orbit spaces
• The Continuous Wavelet Transform and Symmetric Spaces

Related

• Coorbit Theory for Coefficients in Weighted Lebesgue Spaces, and its Application to the Wavelet Transform and the Short-Time Fourier Transform
• A classification of continuous wavelet transforms in dimension three
• On wavelet coorbit spaces associated to different dilation groups
• Coorbit spaces and wavelet coefficient decay over general dilation groups
• Classifying decomposition and wavelet coorbit spaces using coarse geometry