Ebook: Clifford Analysis and Its Applications

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.

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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.

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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.
Content:
Front Matter....Pages i-xii
Riemann-Hilbert Problems in Clifford Analysis....Pages 1-8
The Continuous Wavelet Transform in Clifford Analysis....Pages 9-26
Automated Symbolic Computation in Spin Geometry....Pages 27-38
Monogenic Forms of Polynomial Type....Pages 39-48
On Beltrami Equations in Clifford Analysis and Its Quasi-conformal Solutions....Pages 49-58
Parallel Transport of Algebraic Spinors on Clifford Manifolds....Pages 59-69
On Weighted Spaces of Monogenic Quaternion-valued Functions....Pages 71-80
Plane Waves in Premetric Electrodynamics....Pages 81-89
Contact Symplectic Geometry in Parabolic Invariant Theory and Symplectic Dirac Operator....Pages 91-102
Commimication via Holomorphic Green Functions....Pages 103-111
Hyper-holomorphic Cells and Riemann-Hilbert Problems....Pages 113-121
Nilpotent Lie Groups in Clifford Analysis and Mathematical Physics....Pages 123-133
A Quaternionic Generalization of the Riccati Differential Equation....Pages 135-141
Invariant Operators for Quaternionic Structures....Pages 143-154
On Generalized Clifford Algebras - a Survey of Applications....Pages 155-162
Is the Visual Cortex a “Clifford Algebra Quantum Computer”?....Pages 163-171
Quaternionic Analysis in ?3 Versus Its Hyperbolic Modification....Pages 173-182
Contributions to a Geometric Function Theory in Higher Dimensions by Clifford Analysis Methods: Monogenic Functions and M-conformal mappings....Pages 183-191
The Dirac Type Tensor Equation in Riemannian Space....Pages 193-211
Harmonic Analysis of Dirac Operators on Lipschitz Domains....Pages 213-222
Weight Problems for Higher Dimensional Singular Integrals via Clifford Analysis....Pages 223-230
The Conformal Laplacian on Spheres and Hyperbolas via Clifford Analysis....Pages 231-246
Combinatorics and Clifford analysis....Pages 247-253
The Spherical X-Ray Transform of Texture Goniometry....Pages 255-266
Quaternionic Complexes in Clifford Analysis....Pages 267-282
Clifford Analysis on the Level of Abstract Vector Variables....Pages 283-291
Clifford Analysis as a Study of Invariant Operators....Pages 293-301
Teodorescu Type Transforms in Applications....Pages 303-322
Combinatorics and Clifford Analysis....Pages 323-339
Double Covers of Pseudo-orthogonal Groups....Pages 341-360
Higher Spin Fields on Smooth Domains....Pages 361-376
Bergman Type Spaces on the Unit Disk....Pages 377-388
Back Matter....Pages 389-398
....Pages 399-409