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## ‣ Diffusive wavelets on the Spin group

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Mathematics - Functional Analysis#Mathematics - Complex Variables#Mathematics - Group Theory#Mathematics - Representation Theory#42C40, 43A75, 43A77, 43A85, 43A90

The first part of this article is devoted to a brief review of the results
about representation theory of the spin group Spin(m) from the point of view of
Clifford analysis. In the second part we are interested in Clifford-valued
functions and wavelets on the sphere. The connection of representations of
Spin(m) and the concept of diffusive wavelets leads naturally to investigations
of a modified diffusion equation on the sphere, that makes use of the Gamma
operator. We will achieve to obtain Clifford-valued diffusion wavelets with
respect to a modified diffusion operator.
Since we are able to characterize all representations of Spin(m) and even to
obtain all eigenvectors of the (by representation) regarded Casimir operator in
representation spaces, it seems appropriate to look at functions on Spin(m)
directly. Concerning this, our aim shall be to formulate eigenfunctions for the
Laplace-Beltrami operator on Spin(m) and give the series expansion of the heat
kernel on Spin(m) in terms of eigenfunctions.; Comment: 28 pages. arXiv admin note: text overlap with arXiv:0809.1408 1
reference added, motivation part rewritten

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