Advances in Analysis and Geometry

Tao Qian

ISBN 10: 3764366613 / ISBN 13: 9783764366612

Editore: Springer, Basel, Birkhäuser Basel, Birkhäuser Apr 2004, 2004

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This item is printed on demand - it takes 3-4 days longer - Neuware -On the 16th of October 1843, Sir William R. Hamilton made the discovery of the quaternion algebra H = qo + qli + q2j + q3k whereby the product is determined by the defining relations 2 2 1 Z =] = - , ij = -ji = k. In fact he was inspired by the beautiful geometric model of the complex numbers in which rotations are represented by simple multiplications z ----t az. His goal was to obtain an algebra structure for three dimensional visual space with in particular the possibility of representing all spatial rotations by algebra multiplications and since 1835 he started looking for generalized complex numbers (hypercomplex numbers) of the form a + bi + cj. It hence took him a long time to accept that a fourth dimension was necessary and that commutativity couldn't be kept and he wondered about a possible real life meaning of this fourth dimension which he identified with the scalar part qo as opposed to the vector part ql i + q2j + q3k which represents a point in space. 376 pp. Englisch.

Codice articolo 9783764366612

Dati bibliografici

• Titolo: Advances in Analysis and Geometry
• Editore: Springer, Basel, Birkhäuser Basel, Birkhäuser Apr 2004
• Data di pubblicazione: 2004
• Lingua: Inglese
• ISBN 10: 3764366613
• ISBN 13: 9783764366612
• Rilegatura: Buch
• Condizione: Neu

Descrizione articolo

Riassunto

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 All articles contain unpublished new results.

Contenuti

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.