Ebook: Clifford Algebra and Spinor-Valued Functions: A Function Theory for the Dirac Operator

This volume describes the substantial developments in Clifford analysis which have taken place during the last decade and, in particular, the role of the spin group in the study of null solutions of real and complexified Dirac and Laplace operators.
The book has six main chapters. The first two (Chapters 0 and I) present classical results on real and complex Clifford algebras and show how lower-dimensional real Clifford algebras are well-suited for describing basic geometric notions in Euclidean space. Chapters II and III illustrate how Clifford analysis extends and refines the computational tools available in complex analysis in the plane or harmonic analysis in space. In Chapter IV the concept of monogenic differential forms is generalized to the case of spin-manifolds. Chapter V deals with analysis on homogeneous spaces, and shows how Clifford analysis may be connected with the Penrose transform. The volume concludes with some Appendices which present basic results relating to the algebraic and analytic structures discussed. These are made accessible for computational purposes by means of computer algebra programmes written in REDUCE and are contained on an accompanying floppy disk.

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Content:
Front Matter....Pages i-xvii
Clifford algebras over lower dimensional Euclidean spaces....Pages 1-47
Clifford Algebras and Spinor Spaces....Pages 48-128
Monogenic functions....Pages 129-280
Special functions and methods....Pages 281-356
Monogenic differential forms and residues....Pages 357-387
Clifford analysis and the Penrose transform....Pages 388-430
Back Matter....Pages 431-485

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Content:
Front Matter....Pages i-xvii
Clifford algebras over lower dimensional Euclidean spaces....Pages 1-47
Clifford Algebras and Spinor Spaces....Pages 48-128
Monogenic functions....Pages 129-280
Special functions and methods....Pages 281-356
Monogenic differential forms and residues....Pages 357-387
Clifford analysis and the Penrose transform....Pages 388-430
Back Matter....Pages 431-485
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