Analysis of Dirac systems and computational algebra.
type: Item
instance of: scholarly article
title: Analysis of Dirac systems and computational algebra.
zbMATH Open document ID: 1064.30049
author: Fabrizio Colombo
author: Irene Sabadini
author: Frank Sommen
author: D. C. Struppa
published in: Progress in Mathematical Physics
publication date: 2005-02-18T00:00:00Z
review text: The book contains six chapters and the bibliography. Chapter 1, Background material, provides some necessary material and the most important tools to be used throughout the book. In order to make the book accessible to the readers who are not experts in either the algebraic or analytic aspects, there is given the minimum of exposition of the various needed tools which are usually spread over several books, thus the chapter is divided into three parts: algebraic tools, analytical tools and elements of hyperfunctions theory. The first headings refers to the fundamental notions of commutative algebra that underlie both algebraic geometry and algebraic analysis, the basic notions of sheaf theory, and the foundations of the theory of Gröbner bases. The part on analytical tools assembles the fundamental ideas on the space of distributions. The last section provides the reader with the fundamental notions about hyperfunctions as specific generalized functions. An appendix contains the basic definitions of category theory. It is worth mentioning that although the chapter is intended to be just a collection of auxiliary, for book's main purposes, facts it is nicely written, expresses the author's vision of them from a certain optics and can serve also as a good survey. An analogous observation could be made about Chapter 2, Computational algebraic analysis for systems of linear constant coefficients differential equations: it is a pleasantly readable although in no way trivial overview of those aspects of algebraic analysis which is necessary for understanding the original sections of the book making the latter sufficiently self-closed. The authors note that historically Euler was the first major mathematician to use the term \textit{algebraic analysis} in connection with his important work on general solutions to linear ordinary differential equations with constant coefficients. Currently the term refers to the work of the Japanese school of Kyoto (Sato, Kashiwara, Kawai an…
Mathematics Subject Classification ID: 30G35
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 35Q40
zbMATH DE Number: 2134808
zbMATH Keywords: Dirac systems
zbMATH Keywords: Clifford analysis
zbMATH Keywords: computational algebra
reviewed by: M. Shapiro
describes a project that uses: CoCoA
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2134808