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
Table of Contents:
  • 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