Clifford Algebras and their Applications in Mathematical Physics

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.