Classifying Wavelet Coorbit Spaces in Dimension 2
Noufal Asharaf, Hartmut F\"uhr, Vaishakh Jayaprakash
TL;DR
This paper characterizes when different wavelet systems generate identical coorbit spaces in two dimensions, enhancing understanding of wavelet system equivalences within a rigorous mathematical framework.
Contribution
It provides a comprehensive classification of wavelet systems that produce the same coorbit spaces in dimension two, filling a gap in the theoretical understanding of wavelet equivalences.
Findings
Complete classification of wavelet systems with identical coorbit spaces in 2D
Identification of conditions for equivalence of continuous wavelet transforms
Advancement in the theoretical understanding of wavelet system properties
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.
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