Clifford Wavelets, Singular Integrals, and Hardy Spaces - Marius Mitrea

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Résumé :
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.

Biographie:
Juan Jos? Mar?n is a harmonic analyst whose research interests also include boundary value problems and geometric measure theory. He received a Ph.D. in mathematics in 2019 from Universidad Aut\'onoma de Madrid and Instituto de Ciencias Matem\'aticas, Spain, working under the supervision of Jos? Mar?a Martell and Marius Mitrea. Jos? Mar?a Martell is a mathematician specializing in the areas of harmonic analysis, partial differential equations, and geometric measure theory. He received a Ph.D. in mathematics from Universidad Aut?noma de Madrid, Spain, working under the supervision of Jos? Garcia-Cuerva. Jos? Mar?a Martell is currently serving as the director of Instituto de Matem?ticas, Spain. Dorina Mitrea is a mathematician specializing in the areas of harmonic analysis, partial differential equations, geometric measure theory, and global analysis. She received a Ph.D. in mathematics from the University of Minnesota, working under the supervision of Eugene Fabes. Dorina Mitrea is currently serving as the chair of the Department of Mathematics, Baylor University, USA. Irina Mitrea is an L.H. Carnell Professor and chair of the Department of Mathematics at Temple University whose expertise lies at the interface between the areas of harmonic analysis, partial differential equations, and geometric measure theory. She received her Ph.D. in mathematics from the University of Minnesota, working under the supervision of Carlos Kenig and Mikhail Safanov. Irina Mitrea is a Fellow of the American Mathematical Society and a Fellow of the Association for Women in Mathematics. She received a Simons Foundation Fellowship, a Von Neumann Fellowship at the Institute for Advanced Study, Princeton, and is a recipient of the Ruth Michler Memorial Prize from the Association for Women in Mathematics. Marius Mitrea is a mathematician whose research interests lay at the confluence between harmonic analysis, partial differential equations, geometric measure theory, global analysis, and scattering. He received a Ph.D. in mathematics from the University of South Carolina, USA, working under the supervision of Bj?rn D. Jawerth. Marius Mitrea is a Fellow of the American Mathematical Society.