Analysis of Dirac Systems and Computational Algebra

Fabrizio Colombo, Irene Sabadini, Franciscus Sommen, Daniele C. Struppa - Collection Progress in Mathematical Physics

332 pages, parution le 02/11/2004

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Résumé

The subject of Clifford algebras has become an increasingly rich area of research with a significant number of important applications not only to mathematical physics but to numerical analysis, harmonic analysis, and computer science. The main treatment is devoted to the analysis of systems of linear partial differential equations with constant coefficients, focusing attention on null solutions of Dirac systems. In addition to their usual significance in physics, such solutions are important mathematically as an extension of the function theory of several complex variables. The term "computational" in the title emphasizes two main features of the book, namely, the heuristic use of computers to discover results in some particular cases, and the application of Gröbner bases as a primary theoretical tool. Knowledge from different fields of mathematics such as commutative algebra, Gröbner bases, sheaf theory, cohomology, topological vector spaces, and generalized functions (distributions and hyperfunctions) is required of the reader. However, all the necessary classical material is initially presented. The book may be used by graduate students and researchers interested in (hyper)complex analysis, Clifford analysis, systems of partial differential equations with constant coefficients, and mathematical physics.

Sommaire

Preface
Background Material
Computational Algebraic Analysis for Systems of Linear Constant Coefficients Differential Equations
The Cauchy-Fueter Systems and its Variations
Special First Order Systems in Clifford Analysis
Some First Order Linear Operators in Physics
Open Problems and Avenues for Further Research
References
Index

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	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	Fabrizio Colombo, Irene Sabadini, Franciscus Sommen, Daniele C. Struppa
Collection	Progress in Mathematical Physics
Parution	02/11/2004
Nb. de pages	332
Format	16 x 24
Couverture	Relié
Poids	658g
Intérieur	Noir et Blanc
EAN13	9780817642556
ISBN13	978-0-8176-4255-6