A classification of continuous wavelet transforms in dimension three
Functional Analysis
2016-10-26 v1
Abstract
This paper presents a full catalogue, up to conjugacy and subgroups of finite index, of all matrix groups that give rise to a continuous wavelet transform with associated irreducible quasi-regular representation. For each group in this class, coorbit theory allows to consistently define spaces of sparse signals, and to construct atomic decompositions converging simultaneously in a whole range of these spaces. As an application of the classification, we investigate the existence of compactly supported admissible vectors and atoms for the groups.
Cite
@article{arxiv.1610.07739,
title = {A classification of continuous wavelet transforms in dimension three},
author = {Bradley Currey and Hartmut Führ and Vignon Oussa},
journal= {arXiv preprint arXiv:1610.07739},
year = {2016}
}