Advances in Analysis and Geometry (eBook, PDF)

New Developments Using Clifford Algebras
Redaktion: Qian, Tao; Sommen, Franciscus; Mcintosh, Alan; Hempfling, Thomas

• Format: PDF

Produktbeschreibung

At the heart of Clifford analysis is the study of systems of special partial differential operators that arise naturally from the use of Clifford algebra as a calculus tool. This book focuses on the study of Dirac operators and related ones, together with applications in mathematics, physics and engineering. This book collects refereed papers from a satellite conference to the ICM 2002, plus invited contributions. All articles contain unpublished new results.

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Produktdetails

• Verlag: Birkhäuser Basel
• Seitenzahl: 376
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783034878388
• Artikelnr.: 53141366

Inhaltsangabe

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 BqFunctions.- Pointwise Convergence of Fourier Series on the Unit Sphere of R4with the Quaternionic Setting.- Cauchy Kernels for some Conformally Flat Manifolds.- Clifford Analysis on the Space of Vectors, Bivectors and ?-vectors.- B. Global Analysis and Differential Geometry.- 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.- C. Applications.- 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.