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Clifford Analysis and Its Applications

  • Book
  • © 2001

Overview

Editors:
  1. F. Brackx

    1. Department of Mathematical Analysis, Ghent University, Ghent, Belgium

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  2. J. S. R. Chisholm

    1. Institute of Mathematics and Statistics, University of Kent, Canterbury, UK

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    You can also search for this editor in PubMed   Google Scholar

  3. V. Souček

    1. Mathematical Institute, Charles University, Prague, Czech Republic

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: NATO Science Series II: Mathematics, Physics and Chemistry (NAII, volume 25)

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Table of contents (34 chapters)

  1. Front Matter

    Pages i-xii
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  2. Riemann-Hilbert Problems in Clifford Analysis

    • Swanhild Bernstein
    Pages 1-8

  3. The Continuous Wavelet Transform in Clifford Analysis

    • Fred Brackx, Frank Sommen
    Pages 9-26

  4. Automated Symbolic Computation in Spin Geometry

    • Thomas Branson
    Pages 27-38

  5. Monogenic Forms of Polynomial Type

    • Jarolím Bureš
    Pages 39-48

  6. On Beltrami Equations in Clifford Analysis and Its Quasi-conformal Solutions

    • Paula Cerejeiras, Uwe Kähler
    Pages 49-58

  7. Parallel Transport of Algebraic Spinors on Clifford Manifolds

    • J. S. Roy Chisholm
    Pages 59-69

  8. A Correspondence of Hyperholomorphic and Monogenic Functions in ℝ4

    • Sirkka-Liisa Eriksson-Bique
    Pages 71-80

  9. On Weighted Spaces of Monogenic Quaternion-valued Functions

    • Klaus Gürlebeck
    Pages 81-89

  10. Plane Waves in Premetric Electrodynamics

    • Bernard Jancewicz
    Pages 91-102

  11. Contact Symplectic Geometry in Parabolic Invariant Theory and Symplectic Dirac Operator

    • Lenka Kadlčáková
    Pages 103-111

  12. Commimication via Holomorphic Green Functions

    • Gerald Kaiser
    Pages 113-121

  13. Hyper-holomorphic Cells and Riemann-Hilbert Problems

    • Georg Khimshiashvili
    Pages 123-133

  14. Nilpotent Lie Groups in Clifford Analysis and Mathematical Physics

    • Vladimir V. Kisil
    Pages 135-141

  15. A Quaternionic Generalization of the Riccati Differential Equation

    • Viktor Kravchenko, Vladislav Kravchenko, Benjamin Williams
    Pages 143-154

  16. Invariant Operators for Quaternionic Structures

    • Lukáš Krump
    Pages 155-162

  17. On Generalized Clifford Algebras - a Survey of Applications

    • A. Krzysztof Kwaśniewski
    Pages 163-171

  18. Is the Visual Cortex a “Clifford Algebra Quantum Computer”?

    • Valeri Labunets, Ekaterina Labunets-Rundblad, Jaakko Astola
    Pages 173-182

  19. The Cl n -Valued Robin Boundary Value Problem on Lipschitz Domains in ℝ n

    • Loredana Lanzani
    Pages 183-191

  20. Quaternionic Analysis in ℝ3 Versus Its Hyperbolic Modification

    • Heinz Leutwiler
    Pages 193-211
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Keywords

About this book

In its traditional form, Clifford analysis provides the function theory for solutions of the Dirac equation. From the beginning, however, the theory was used and applied to problems in other fields of mathematics, numerical analysis, and mathematical physics. recently, the theory has enlarged its scope considerably by incorporating geometrical methods from global analysis on manifolds and methods from representation theory. New, interesting branches of the theory are based on conformally invariant, first-order systems other than the Dirac equation, or systems that are invariant with respect to a group other than the conformal group. This book represents an up-to-date review of Clifford analysis in its present form, its applications, and directions for future research.
Readership: Mathematicians and theoretical physicists interested in Clifford analysis itself, or in its applications to other fields.

Editors and Affiliations

  • Department of Mathematical Analysis, Ghent University, Ghent, Belgium

    F. Brackx

  • Institute of Mathematics and Statistics, University of Kent, Canterbury, UK

    J. S. R. Chisholm

  • Mathematical Institute, Charles University, Prague, Czech Republic

    V. Souček

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