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Analysis of Dirac Systems and Computational Algebra
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Analysis of Dirac Systems and Computational Algebra

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

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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Caractéristiques techniques

  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

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