Research Catalog

Analysis of Dirac systems and computational algebra

Title
Analysis of Dirac systems and computational algebra / Fabrizio Colombo [and others].
Publication
Boston : Birkhäuser, [2004], ©2004.

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Additional Authors
Colombo, Fabrizio.
Description
xiv, 332 pages; 25 cm.
Summary
"The main treatment in this work 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 Grobner bases as a primary theoretical tool." "Knowledge from different fields of mathematics such as commutative algebra, Grobner 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."--BOOK JACKET.
Series Statement
Progress in mathematical physics ; v. 39
Uniform Title
Progress in mathematical physics ; v. 39.
Subject
  • Mathematical physics
  • Dirac equation
  • Clifford algebras
  • Differential equations, Partial
  • Mathematical analysis
Bibliography (note)
  • Includes bibliographical references (p. [313]-326) and index.
Contents
1. Background material -- 2. Computational algebraic analysis -- 3. The Cauchy-Fueter system and its variations -- 4. Special first order systems in Clifford analysis -- 5. Some first order linear operators in physics -- 6. Open problems and avenues for further research.
ISBN
0817642552 (acid-free paper)
LCCN
2004053657
OCLC
  • ocm55665319
  • SCSB-5124550
Owning Institutions
Columbia University Libraries