Research Catalog

Title

Analysis of Dirac systems and computational algebra / Fabrizio Colombo [and others].

Publication

Boston : Birkhäuser, [2004], ©2004.

Items in the Library & Off-site

Details

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.

Subjects

• Mathematical analysis
• Dirac equation
• Mathematical physics
• Clifford algebras
• Differential equations, Partial

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