Analysis of Dirac Systems and Computational Algebra
By: by Fabrizio Colombo, Irene Sabadini, Franciscus Sommen, Daniele C. Struppa
Contributors: Sabadini, Irene; Sommen, Franciscus; Struppa, Daniele C.
Series: Progress in Mathematical Physics -- 39; Progress in mathematical physics -- 39.
Publisher: Birkhäuser Boston; Imprint: Birkhäuser
Published: 2004
Place of publication: Boston, MA
Language: eng
Format: [electronic resource] /
Number of pages: 332
ISBN-13: 9781461264699; 9780817681661
Subjects: Mathematics; Mathematical physics; Matrix theory; Partial Differential equations
Description: 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.
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Table of contents: title: Preface; title: Background Material; title: Computational Algebraic Analysis for Systems of Linear Constant Coefficients Differential Equations; title: The Cauchy-Fueter Systems and its Variations; title: Special First Order Systems in Clifford Analysis; title: Some First Order Linear Operators in Physics; title: Open Problems and Avenues for Further Research; title: References; title: Index.