A Classification of Continuous Wavelet Transforms in Dimension Three
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.
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]
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: http://vc.bridgew.edu/math_fac/66