1 Partial Differential Equations and Boundary Value Problems.- On Quaternionic Beltrami Equations.- The M bius Transformation, Green Function and the Degenerate Elliptic Equation.- Quaternionic Analysis in Fluid Mechanics.- 2 singular Integral Operators.- Fourier Theory Under M bius 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 M bius Transformations and Monogenic Functions.- The Schwarzian and M bius 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.
Inhaltsverzeichnis
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.
