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Diffusive wavelets on groups and homogeneous spaces

Published online by Cambridge University Press:  03 June 2011

Svend Ebert  and
Jens Wirth
Svend Ebert
Affiliation:
Institut für Angewandte Analysis, TU Bergakademie Freiberg, 09596 Freiberg, Germany ([email protected])
Jens Wirth
Affiliation:
Institut für Analysis, Dynamik und Modellierung, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany ([email protected])
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Abstract

We explain the 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 the Peter-Weyl decomposition of L2() for a compact Lie group . After developing a general concept for compact groups and their homogeneous spaces, we give concrete examples for tori, which reflect the situation on ℝn, and for 2 and 3 spheres.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 141 , Issue 3 , June 2011 , pp. 497 - 520
Copyright
Copyright © Royal Society of Edinburgh 2011

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