Analysis of Dirac Systems and Computational Algebra

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 linea...

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Main Authors: Colombo, Fabrizio, Sabadini, Irene (Author), Sommen, Franciscus (Author), Struppa, Daniele C. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Boston, MA Birkhäuser Boston 2004, 2004
Edition:1st ed. 2004
Series:Progress in Mathematical Physics
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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100 1 |a Colombo, Fabrizio 
245 0 0 |a Analysis of Dirac Systems and Computational Algebra  |h Elektronische Ressource  |c by Fabrizio Colombo, Irene Sabadini, Franciscus Sommen, Daniele C. Struppa 
250 |a 1st ed. 2004 
260 |a Boston, MA  |b Birkhäuser Boston  |c 2004, 2004 
300 |a XV, 332 p  |b online resource 
505 0 |a category theory -- 2 Computational Algebraic Analysis -- 2.1 A primer of algebraic analysis -- 2.2 The Ehrenpreis-Palamodov Fundamental Principle -- 2.3 The Fundamental Principle for hyperfunctions -- 2.4 Using computational algebra software -- 3 The Cauchy-Fueter System and its Variations -- 3.1 Regular functions of one quaternionic variable -- 3.2 Quaternionic hyperfunctions in one variable -- 3.3 Several quaternionic variables: analytic approach -- 3.4 Several quaternionic variables: an algebraic approach -- 3.5 The Moisil-Theodorescu system -- 4 Special First Order Systems in Clifford Analysis -- 4.1 Introduction to Clifford algebras -- 4.2 Introduction to Clifford analysis -- 4.3 The Dirac complex for two, three and four operators -- 4.4 Special systems in Clifford analysis -- 5 Some First Order Linear Operators in Physics -- 5.1 Physics and algebra of M 
653 |a Linear and Multilinear Algebras, Matrix Theory 
653 |a Partial Differential Equations 
653 |a Algebra 
653 |a Numerical and Computational Physics, Simulation 
653 |a Algebra 
653 |a Physics 
653 |a Mathematical Methods in Physics 
653 |a Partial differential equations 
653 |a Matrix theory 
700 1 |a Sabadini, Irene  |e [author] 
700 1 |a Sommen, Franciscus  |e [author] 
700 1 |a Struppa, Daniele C.  |e [author] 
710 2 |a SpringerLink (Online service) 
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490 0 |a Progress in Mathematical Physics 
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082 0 |a 512 
520 |a 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