Clifford Wavelets, Singular Integrals, and Hardy Spaces
Mitrea, Marius.
Clifford Wavelets, Singular Integrals, and Hardy Spaces [electronic resource] / by Marius Mitrea. - CXXXVI, 124 p. online resource. - Lecture Notes in Mathematics, 1575 0075-8434 ; . - Lecture Notes in Mathematics, 1575 .
Clifford algebras -- Constructions of Clifford wavelets -- The L 2 Boundedness of Clifford algebra valued singular integral operators -- Hardy spaces of monogenic functions -- Applications to the theory of harmonic functions.
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.
9783540483793
10.1007/BFb0073556 doi
Global analysis (Mathematics).
Analysis.
QA299.6-433
515
Clifford Wavelets, Singular Integrals, and Hardy Spaces [electronic resource] / by Marius Mitrea. - CXXXVI, 124 p. online resource. - Lecture Notes in Mathematics, 1575 0075-8434 ; . - Lecture Notes in Mathematics, 1575 .
Clifford algebras -- Constructions of Clifford wavelets -- The L 2 Boundedness of Clifford algebra valued singular integral operators -- Hardy spaces of monogenic functions -- Applications to the theory of harmonic functions.
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.
9783540483793
10.1007/BFb0073556 doi
Global analysis (Mathematics).
Analysis.
QA299.6-433
515