Clifford Wavelets, Singular Integrals, and Hardy Spaces

Marius Mitrea (auth.)9780387578842, 0-387-57884-6

The book discusses the extensions of basic Fourier Analysis techniques to the Clifford algebra framework.
Topics covered: construction of Clifford-valued wavelets, Calderon-Zygmund theory for Clifford valued singular integral operators on Lipschitz hyper-surfaces, Hardy spaces of Clifford monogenic functions on Lipschitz domains. Results are applied to potential theory and elliptic boundary value problems on non-smooth domains. The book is self-contained to a large extent and well-suited for graduate students and researchers in the areas of wavelet theory, Harmonic and Clifford Analysis.
It will also interest the specialists concerned with the applications of the Clifford algebra machinery to Mathematical Physics.

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Table of contents :
Clifford algebras….Pages 1-15
Constructions of Clifford wavelets….Pages 16-41
The L 2 Boundedness of Clifford algebra valued singular integral operators….Pages 42-59
Hardy spaces of monogenic functions….Pages 60-86
Applications to the theory of harmonic functions….Pages 87-105