Title

A Classification of Continuous Wavelet Transforms in Dimension Three

Publication Date

2016

Document Type

Article

Abstract

This paper presents a full catalogue, up to conjugacy and subgroups of finite index, of all matrix groups H < GL(3,ℝ) 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.

Original Citation

Currey, B., Fuhr, H., & Oussa, V. (2016). A Classification of Continuous Wavelet Transforms in Dimension Three. Published October 25, 2016. arXiv:1610.07739v1 [math.FA]

Identifier

arXiv: 1610.07739v1 [math.FA]