Diffusive wavelets on groups and homogeneous spaces

TL;DR

This paper explains the construction of diffusive wavelets on spheres and homogeneous spaces using representation theory and Fourier analysis on compact Lie groups, providing concrete examples for tori and spheres.

Contribution

It introduces a general framework for diffusive wavelets on compact groups and homogeneous spaces, with explicit examples on tori and spheres, connecting wavelet theory with Lie group representations.

Findings

Development of a general concept for diffusive wavelets on compact groups

Concrete examples of wavelets on tori, spheres S^2 and S^3

Application of representation theory and Fourier analysis in wavelet construction

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 $S^3$.