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Overview* 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 Full Product DetailsAuthor: Fabrizio Colombo , Irene Sabadini , Franciscus Sommen , Daniele C. StruppaPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: Softcover reprint of the original 1st ed. 2004 Volume: 39 Dimensions: Width: 15.50cm , Height: 1.80cm , Length: 23.50cm Weight: 0.539kg ISBN: 9781461264699ISBN 10: 1461264693 Pages: 332 Publication Date: 04 October 2012 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of Contents1 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.ReviewsFrom the reviews: The book presents a uniform treatment of some fundamental differential equations for physics. Maxwell and Dirac equations are particular examples that fall into this study. The authors concentrate on systems of linear partial differential equations with constatn coefficients n the Clifford algebra setting...The material is presented in a very accessible format...The book ends with a list of open problems that pertain to the topic. ---Internationale Mathematische Nachrichten, Nr. 201 The first 138 pages of this book are a good introduction to algebraic analysis (in the sense of Sato), and some computational aspects, in the setting of quaternionic analysis. But the core of the book is the study of different important systems of partial differential equations in the setting of Clifford analysis...The last chapter states some open problems and avenues of further research. A rich list of references, an alphabetic index and a list of notation close the volume. Well-written and with many explicit results, the book is interesting and is addressed to Ph.D. students and researchers interested in this field. ---Revue Roumaine de Mathematiques Pures et Appliquees Altogether the book is a pioneering, and quite successful, attempt to apply computational and algebraic techniques to several branches of hypercomplex analysis ... The book provides a very different way to look at some important questions which arise when one tries to develop multi-dimensional theories. (MATHEMATICAL REVIEWS) From the reviews: The book presents a uniform treatment of some fundamental differential equations for physics. Maxwell and Dirac equations are particular examples that fall into this study. The authors concentrate on systems of linear partial differential equations with constatn coefficients n the Clifford algebra setting...The material is presented in a very accessible format...The book ends with a list of open problems that pertain to the topic. ---Internationale Mathematische Nachrichten, Nr. 201 The first 138 pages of this book are a good introduction to algebraic analysis (in the sense of Sato), and some computational aspects, in the setting of quaternionic analysis. But the core of the book is the study of different important systems of partial differential equations in the setting of Clifford analysis...The last chapter states some open problems and avenues of further research. A rich list of references, an alphabetic index and a list of notation close the volume. Well-written and with many explicit results, the book is interesting and is addressed to Ph.D. students and researchers interested in this field. ---Revue Roumaine de Mathematiques Pures et Appliquees Altogether the book is a pioneering, and quite successful, attempt to apply computational and algebraic techniques to several branches of hypercomplex analysis ... The book provides a very different way to look at some important questions which arise when one tries to develop multi-dimensional theories. (MATHEMATICAL REVIEWS) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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