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Analysis of Dirac Systems and Computational Algebra

  • Fabrizio Colombo
  • Irene Sabadini
  • Franciscus Sommen
  • Daniele C. Struppa

Part of the Progress in Mathematical Physics book series (PMP, volume 39)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Fabrizio Colombo, Irene Sabadini, Franciscus Sommen, Daniele C. Struppa
    Pages 1-91
  3. Fabrizio Colombo, Irene Sabadini, Franciscus Sommen, Daniele C. Struppa
    Pages 93-138
  4. Fabrizio Colombo, Irene Sabadini, Franciscus Sommen, Daniele C. Struppa
    Pages 139-207
  5. Fabrizio Colombo, Irene Sabadini, Franciscus Sommen, Daniele C. Struppa
    Pages 209-266
  6. Fabrizio Colombo, Irene Sabadini, Franciscus Sommen, Daniele C. Struppa
    Pages 267-306
  7. Fabrizio Colombo, Irene Sabadini, Franciscus Sommen, Daniele C. Struppa
    Pages 307-311
  8. Back Matter
    Pages 313-332

About this book

Introduction

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.

Keywords

Algebra Category theory Cohomology Complex Analysis Differential Equations Numerical & Computational Tech Quantum Field Theory mathematical physics partial differential equation

Authors and affiliations

  • Fabrizio Colombo
    • 1
  • Irene Sabadini
    • 1
  • Franciscus Sommen
    • 2
  • Daniele C. Struppa
    • 3
  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  2. 2.Faculty of Engineering Department of Mathematical AnalysisGhent UniversityGhentBelgium
  3. 3.Department of Mathematical SciencesGeorge Mason UniversityFairfaxUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-8166-1
  • Copyright Information Springer Science+Business Media New York 2004
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6469-9
  • Online ISBN 978-0-8176-8166-1
  • Buy this book on publisher's site