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Clifford Algebras in Analysis and Related Topics : Studies in Advanced Mathematics - John Ryan

Clifford Algebras in Analysis and Related Topics

Studies in Advanced Mathematics

By: John Ryan

Hardcover Published: 23rd October 1995
ISBN: 9780849384813
Number Of Pages: 384

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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.

Acknowledgmentp. 1
Conference Participantsp. 3
Introductionp. 7
Problem Bookp. 17
Clifford Algebras, Fourier Theory, Singular Integrals, and Harmonic Functions on Lipschitz Domainsp. 33
Clifford Algebras and H[actual symbol not reproducible] Functional Calculi of Commuting Operatorsp. 89
Hypercomplex Variable Techniques in Harmonic Analysisp. 103
Some Applications of Conformal Covariance in Clifford Analysisp. 129
Singular Integrals with Monogenic Kernels on the m-Torus and their Lipschitz Perturbationsp. 157
Scattering Theory for Orthogonal Waveletsp. 173
Acoustic Scattering, Galerkin Estimates and Clifford Algebrasp. 199
Clifford Algebras, Hardy Spaces, and Compensated Compactnessp. 217
Frame Decompositions of Form-Valued Hardy Spacesp. 239
Applications of Clifford Analysis to Inverse Scattering for the Linear Hierarchy in Several Space Dimensionsp. 261
On Riemann-Hilbert Problems for Nonhomogeneous Dirac Equations in a Half Space of [actual symbol not reproducible]p. 285
Regularity and Approximation Results for the Maxwell Problem on C[superscript 1] and Lipschitz Domainsp. 297
Continuity of Calderon-Zygmund Type Operators on the Predual of a Morrey Spacep. 309
Neumann Type Problems for the Dirac Operatorp. 321
The Hyperholomorphic Bergman Projector and its Propertiesp. 333
Multivector Solutions to the Hyperholomorphic Massive Dirac Equationp. 345
Mobius Transformations, Vahlen Matrices, and their Factorizationp. 361
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780849384813
ISBN-10: 0849384818
Series: Studies in Advanced Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 384
Published: 23rd October 1995
Publisher: CRC PR INC
Country of Publication: US
Dimensions (cm): 24.13 x 16.51  x 2.54
Weight (kg): 0.7
Edition Number: 1

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