Clifford algebras in analysis and related topics : Based on a conference held in Fayetteville, Arkansas during the weekend, April 8-10th, 1993

This new book contains the most up-to-date and focused description of the applications of Clifford algebras in analysis, particularly classical harmonic analysis. It is the first single volume devoted to applications of Clifford analysis to other aspects of analysis. All chapters are written by world authorities in the area. Of particular interest is the contribution of Professor Alan McIntosh. He gives a detailed account of the links between Clifford algebras, monogenic and harmonic functions and the correspondence between monogenic functions and holomorphic functions of several complex variables under Fourier transforms. He describes the correspondence between algebras of singular integrals on Lipschitz surfaces and functional calculi of Dirac operators on these surfaces. He also discusses links with boundary value problems over Lipschitz domains. Other specific topics include Hardy spaces and compensated compactness in Euclidean space; applications to acoustic scattering and Galerkin estimates; scattering theory for orthogonal wavelets; applications of the conformal group and Vahalen matrices; Newmann type problems for the Dirac operator; plus much, much more! Clifford Algebras in Analysis and Related Topics also contains the most comprehensive section on open problems available. The book presents the most detailed link between Clifford analysis and classical harmonic analysis. It is a refreshing break from the many expensive and lengthy volumes currently found on the subject. Booknews Based on a conference held in Fayetteville, Arkansas, April 1993, this proceedings volume contain descriptions of the applications of Clifford algebras in analysis, primarily the impact of Clifford analysis on harmonic analysis. Of particular interest is the paper based on the lectures of principal speaker Alan McIntosh, of Macquarie U., Australia, which provides a detailed account of the links between Clifford algebras, monogenic and harmonic functions, and the correspondence between monogenic functions and holomorphic functions of several complex variables under Fourier transforms. No index. Annotation c. Book News, Inc., Portland, OR (booknews.com) Content: 1. Acknowledgment -- 2. Conference Participants -- 3. Introduction / John Ryan -- 4. Problem Book / H. Blaine Lawson -- 5. Clifford Algebras, Fourier Theory, Singular Integrals, and Harmonic Functions on Lipschitz Domains / Alan McIntosh -- 6. Clifford Algebras and H[actual symbol not reproducible] Functional Calculi of Commuting Operators / Chun Li and Alan McIntosh -- 7. Hypercomplex Variable Techniques in Harmonic Analysis / Marius Mitrea -- 8. Some Applications of Conformal Covariance in Clifford Analysis / John Ryan -- 9. Singular Integrals with Monogenic Kernels on the m-Torus and their Lipschitz Perturbations / Tao Qian -- 10. Scattering Theory for Orthogonal Wavelets / Palle E.T. Jorgensen -- 11. Acoustic Scattering, Galerkin Estimates and Clifford Algebras / Bjorn Jawerth and Marius Mitrea -- 12. Clifford Algebras, Hardy Spaces, and Compensated Compactness / Zhijian Wu.