Advances in Analysis and Geometry: New Developments Using Clifford AlgebrasAuthor: Tao Qian, Thomas Hempfling, Alan McIntosh, Frank Sommen Published by Birkhäuser Basel ISBN: 978-3-0348-9589-7 DOI: 10.1007/978-3-0348-7838-8Table of Contents: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 Universal Bochner-Weitzenböck Formulas for Hyper-Kählerian Gradients Cohomology Groups of Harmonic Spinors on Conformally Flat Manifolds Spin Geometry, Clifford Analysis, and Joint Seminormality A Mean Value Laplacian for Strongly Kähler-Finsler Manifolds Non-commutative Determinants and Quaternionic Monge-Ampère 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, Preface -- Differential Equations and Operator Theory -- Global Analysis and Differential Geometry -- Applications, 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. All articles were strictly refereed and contain unpublished new results. Some of them are incorporated with comprehensive surveys in the particular areas that the authors work in