Diffusive wavelets on groups and homogeneous spaces

Details Diffusive wavelets on groups and homogeneous spaces Diffusive wavelets on groups and homogeneous spaces

2010-03-03

arxiv.org/abs/1003.0860v1

Proceedings of the Royal Society of Edinburgh, Sect. A, 141A (2011) 497-520

Mathematics

Functional Analysis

20 pages, 3 figures

Scientific paper

10.1017/S030821051000051X

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 $S^3$.

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