Clifford Analysis and Its Applications

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

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.

• Boundary value problem
• Singular integral
• harmonic analysis
• linear optimization
• manifold
• symplectic geometry
• partial differential equations

• 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