Analysis of Dirac Systems and Computational Algebra

Fabrizio Colombo, Irene Sabadini, Franciscus Sommen, Daniele C. Struppa (Autoren)

Buch | Softcover

332 Seiten

2012 | Softcover reprint of the original 1st ed. 2004
Springer-Verlag New York Inc.
978-1-4612-6469-9 (ISBN)

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* The main treatment is devoted to the analysis of systems of linear partial differential equations (PDEs) with constant coefficients, focusing attention on null solutions of Dirac systems * All the necessary classical material is initially presented * Geared toward graduate students and researchers in (hyper)complex analysis, Clifford analysis, systems of PDEs with constant coefficients, and mathematical physics

1 Background Material.- 1.1 Algebraic tools.- 1.2 Analytical tools.- 1.3 Elements of hyperfunction theory.- 1.4 Appendix: 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 Maxwell and Proca fields.- 5.2 Variations on Maxwell system in the space of biquaternions.- 5.3 Properties of DZ-regular functions.- 5.4 The Dirac equation and the linearization problem.- 5.5 Octonionic Dirac equation.- 6 Open Problems and Avenues for Further Research.- 6.1 The Cauchy-Fueter system.- 6.2 The Dirac system.- 6.3 Miscellanea.

Reihe/Serie	Progress in Mathematical Physics ; 39
Zusatzinfo	XV, 332 p.
Verlagsort	New York
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie
ISBN-10	1-4612-6469-3 / 1461264693
ISBN-13	978-1-4612-6469-9 / 9781461264699
Zustand	Neuware