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]
Virtual Commons Citation
Currey, Bradley; Fuhr, Hartmut; and Oussa, Vignon (2016). A Classification of Continuous Wavelet Transforms in Dimension Three. In Mathematics Faculty Publications. Paper 66.
Available at: https://vc.bridgew.edu/math_fac/66