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320 pages, vol.2, year 2000, contributed volume by several authors

Abstract:

The vol2 on Clifford Analysis is "an up-to-date survey of most aspects of modern-day Clifford analysis". Topics range widely from applications such as Fourier analysis and the study of boundary value problems to complex-distance potential theory, fluid dynamics and supersymmetry. Highlighted topics are: an unified framework of the Standard Model of particle physics (SUSY) in terms of the Geometry of generalized Dirac operators, Fourier theory under M\"obius transformations, the Schwarzian and M\"obius Transformations in Higher Dimensions, an extension of Cliffor analysis towards super-symmetry, Hypermomogenic functions, Hypercomplex derivability, Holonomy group representations, Inverse Scattering Theory, Convolution in Clifford analysis. Quote from book's Contents: "Contents:... The Mobius Transformation Green Function and the Degenerate p. 17; Dirichlet problem, elliptic equation, Green function ; Quaternionic Analysis in Fluid Mechanics p. 37; Navier-Stokes equations, boundary value problems, viscosity Singular Integral Operators p. 55; Dirac operator, holomorphic functional calculus, Lipschitz domain On the Cauchy Type Integral and the Riemann Problem 81 Riemann problem, boundary value problem, Cauchy kernel Convolution and Maximal Operator Inequalities in Clifford Analysis p. 95 Lebesgue spaces, compact set, Rm+1; Applications in Geometry and Physics p.115 ; Bochner-Martinelli formula, several complex variables, complex analysis.The Mobius Transformation Green Function and the Degenerate 17 Dirichlet problem, elliptic equation, Green function Quaternionic Analysis in Fluid Mechanics 37 Navier-Stokes equations, boundary value problems, viscosity Singular Integral Operators 55 Dirac operator, holomorphic functional calculus, Lipschitz domain On the Cauchy Type Integral and the Riemann Problem 81 Riemann problem, boundary value problem, Cauchy kernel Convolution and Maximal Operator Inequalities in Clifford Analysis 95 Lebesgue spaces, compact set, Rm+1 Applications in Geometry and Physics 115 Bochner-Martinelli formula, several complex variables, complex analysis, Complex Distance Potential Theory and Hyperbolic Equations 135 spacetime, holomorphic, oblate spheroidal coordinates Specific Representations for Members of the Holonomy Group 171 Holonomy Group, Riemann curvature tensor, recursion relation An Extension of Clifford Analysis Towards Supersymmetry 199 fermionic, wedge product, bosonic The Geometry of Generalized Dirac Operators and the Standard 225 Clifford module, fermionic, Riemannian manifold Mobius Transformations and Monogenic p. 237; Schwarzian derivative, Riemannian manifolds; Osamu Kobayashi The Structure of Monogenic Functions p.247; Laplace operator, conformal group, symmetry operators On the Radial Part of the Cauchy-Riemann Operator p.261 paravector, Poincare metric, hypermonogenic Hypercomplex Derivability The Characterization of Monogenic p. 273 differential forms, Hodge star operator, p-forms Hypermonogenic Functions p.287; open subset, homogeneous polynomial, hypermonogenic Reproducing Kernels for Hyperbolic Spaces ;p.303 hyperbolic spaces; Tao Qian, Conformal mappings. Index" \\Key terms: Clifford algebra, Dirac operator, monogenic functions, quaternionic, hypercomplex, fermionic, Cauchy kernel, Schwarzian derivatives, singular integral operator, paravector, differential forms, Mobius transformations, Riemannian manifold, boundary value problem, Clifford module, Dirichlet problem, spinor, complex analysis, Lipschitz domain. Popular passages VV Kravchenko and MV Shapiro, Integral representations for spatial models of mathematical physics, Pitman Research Notes in Mathematics Series 351, - Page 14.\\ Cited in: Martin, M. and Szeptycki, P., Sharp inequalities for convolution operators with homogeneous kernels and applications, Indiana Univ. Math. - Page 113 A. Erdilyi, W. Magnus, F. Oberhettinger, and FG Tricomi, Higher Transcendental Functions, Vols. I, II, - Page 35. 6th International Conference on Clifford Algebras, TTU, Cookeville, Tennessee Technological University, Cookeville, Tennessee, USA. Preliminary lectures 18--19 May, Conference 20--25 May 2002 www.math.tntech.edu/rafal/cookeville/cookeville.html AMS MSC: 15-00 (Linear and multilinear algebra; matrix theory :: General reference works ) 15A66 (Linear and multilinear algebra; matrix theory :: Clifford algebras, spinors) 11E88 (Number theory :: Forms and linear algebraic groups :: Quadratic spaces; Clifford algebras)

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