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

Front Matter....Pages i-xxii
Front Matter....Pages 1-1
On Quaternionic Beltrami Equations....Pages 3-15
The Möbius Transformation, Green Function and the Degenerate Elliptic Equation....Pages 17-35
Quaternionic Analysis in Fluid Mechanics....Pages 37-53
Front Matter....Pages 55-55
Fourier Theory Under Möbius Transformations....Pages 57-80
On the Cauchy Type Integral and the Riemann Problem....Pages 81-94
Convolution and Maximal Operator Inequalities in Clifford Analysis....Pages 95-113
Front Matter....Pages 115-115
A Borel-Pompeiu Formula in ℂ n and Its Application to Inverse Scattering Theory....Pages 117-134
Complex-Distance Potential Theory and Hyperbolic Equations....Pages 135-169
Specific Representations for Members of the Holonomy Group....Pages 171-198
An Extension of Clifford Analysis Towards Super-symmetry....Pages 199-224
The Geometry of Generalized Dirac Operators and the Standard Model of Particle Physics....Pages 225-236
Front Matter....Pages 237-237
The Schwarzian and Möbius Transformations in Higher Dimensions....Pages 239-246
The Structure of Monogenic Functions....Pages 247-260
On the Radial Part of the Cauchy-Riemann Operator....Pages 261-271
Hypercomplex Derivability — The Characterization of Monogenic Functions in ℝ n+1 by Their Derivative....Pages 273-285
Hypermonogenic Functions....Pages 287-302
Reproducing Kernels for Hyperbolic Spaces....Pages 303-314
Back Matter....Pages 315-320