Diffusive wavelets on groups and homogeneous spaces

Abstract

The aim of this exposition is to explain basic ideas behind the concept of diffusive wavelets on spheres in the language of representation theory of Lie groups and within the framework of the group Fourier transform given by Peter-Weyl decomposition of $L^2(G)$ for a compact Lie group $G$. After developing a general concept for compact groups and their homogeneous spaces we give concrete examples for tori -which reflect the situation on $R^n$- and for spheres $S^2$ and $S^3$.

20 pages, 3 figures

Cited by in corpus (6)

• Continuous wavelet transforms on $n$-dimensional spheres
• Poisson wavelets on $n$-dimensional spheres
• Gabor frames from contact geometry in models of the primary visual cortex
• Multiresolution on n-dimensional spheres
• Multifractal Analysis of functions on Heisenberg and Carnot Groups
• Density estimation on the rotation group using diffusive wavelets