Advances in analysis and geometry : new developments using clifford algebras分析和几何进展
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作者： Tao Qian等著
出 版 社：
出版时间： 2004-6-1字数：版次： 1页数： 376印刷时间： 2004/06/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9783764366612包装： 精装内容简介
The study of systems of special partial differential operators that arise naturally from the use of Clifford algebra as a calculus tool lies in the heart of Clifford analysis. The focus is on the study of Dirac operators and related ones, together with applications in mathematics, physics and engineering. At the present time, the study of Clifford algebra and Clifford analysis has grown into a major research field. There are two sources of papers in this collection. One is from a satellite conference to the ICM 2002 in Beijing, held August 15-18 at the University of Macau; and the other stems from invited contributions by top-notch experts in the field.
目录
Preface v
Part A. Differential Equations and Operator Theory
Hodge Decompositions on Weakly Lipschitz Domains
Monogenic Functions of Bounded Mean Oscillation in the Unit Ball
Bp,q-Functions and their Harmonic Majorants
Spherical Means and Distributions in Clifford Analysis
Hypermonogenic Functions and their Cauchy-Type Theorems
On Series Expansions of Hyperholomorphic Bq Functions
Pointwise Convergence of Fourier Series on the Unit Sphere of R4 with the Quaternionic Setting
Cauchy Kernels for some Conformally Flat Manifolds
Clifford Analysis on the Space of Vectors, Bivectors and l-vectors
Part B. Global Analysis and Differential Geometry
Universal Bochner-Weitzenbock Formulas for Hyper-Kahlerian Gradients
Cohomology Groups of Harmonic Spinors on Conformally Flat Manifolds
Spin Geometry, Clifford Analysis, and Joint Seminormality
A Mean Value Laplacian for Strongly Kahler--Finsler Manifolds
Part C. Applications
Non-commutative Determinants and Quatermonic Monge-Ampere Equations
Galpern-Sobolev Type Equations with Non-constant Coefficients
A Theory of Modular Forms in Clifford Analysis, their Applications and Perspectives
Automated Geometric Theorem Proving, Clifford Bracket Algebra and Clifford Expansions
Quaternion-valued Smooth Orthogonal Wavelets with Short Support and Symmetry