Clifford Algebras and Their Applications in Mathematical Physics: Volume 2: Clifford Analysis

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Overview

1 Partial Differential Equations and Boundary Value Problems.- On Quaternionic Beltrami Equations.- The Möbius Transformation, Green Function and the Degenerate Elliptic Equation.- Quaternionic Analysis in Fluid Mechanics.- 2 singular Integral Operators.- Fourier Theory Under Möbius Transformations.- On the Cauchy Type Integral and the Riemann Problem.- Convolution and Maximal Operator Inequalities in Clifford Analysis.- 3 Applications in Geometry and Physics.- A Borel-Pompeiu Formula in ?n and Its Application to Inverse Scattering Theory.- Complex-Distance Potential Theory and Hyperbolic Equations.- Specific Representations for Members of the Holonomy Group.- An Extension of Clifford Analysis Towards Super-symmetry.- The Geometry of Generalized Dirac Operators and the Standard Model of Particle Physics.- 4 Möbius Transformations and Monogenic Functions.- The Schwarzian and Möbius Transformarions in Higher Dimensions.- The Structure of Monogenic Functions.- On the Radial Part of the Cauchy-Riemann Operator.- Hypercomplex Derivability - The Characterization of Monogenic Functions in ?n+1 by Their Derivative.- Hypermonogenic Functions.- Reproducing Kernels for Hyperbolic Spaces.