Clifford Algebras in Analysis and Related Topics

John Ryan

• Publisher: CRC Press
• Year: 2018
• eBook ISBN: 9781351460279
• Topic: Mathematik
• Subtopic: Algebra

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.

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• 1 Acknowledgment
• 2 Conference Participants
• 3 Introduction
• 4 Problem Book
• 5 Clifford Algebras, Fourier Theory, Singular Integrals, and Harmonic Functions on Lipschitz Domains
• 6 Clifford Algebras and H∞ Functional Calculi of Commuting Operators
• 7 Hypercomplex Variable Techniques in Harmonic Analysis
• 8 Some Applications of Conformal Covariance in Clifford Analysis
• 9 Singular Integrals with Monogenic Kernels on the m-Torus and their Lipschitz Perturbations
• 10 Scattering Theory for Orthogonal Wavelets
• 11 Acoustic Scattering, Galerkin Estimates and Clifford Algebras
• 12 Clifford Algebras, Hardy Spaces, and Compensated Compactness
• 13 Frame Decompositions of Form-Valued Hardy Spaces
• 14 Applications of Clifford Analysis to Inverse Scattering for the Linear Hierarchy in Several Space Dimensions
• 15 On Riemann-Hilbert Problems for Nonhomogeneous Dirac Equations in a Half Space of Rm(m > 2)
• 16 Regularity and Approximation Results for the Maxwell Problem on C1 and Lipschitz Domains
• 17 Continuity of Calderón-Zygmund Type Operators on the Predual of a Morrey Space
• 18 Neumann Type Problems for the Dirac Operator
• 19 The Hyperholomorphic Bergman Projector and its Properties
• 20 Multivector Solutions to the Hyperholomorphic Massive Dirac Equation
• 21 Möbius Transformations, Vahlen Matrices, and their Factorization