Analysis of Dirac Systems and Computational Algebra:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
2004
|
| Schriftenreihe: | Progress in Mathematical Physics
39 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1007/978-0-8176-8166-1 |
| Beschreibung: | 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 |
| Umfang: | 1 Online-Ressource (XV, 332 p) |
| ISBN: | 9780817681661 9781461264699 |
| DOI: | 10.1007/978-0-8176-8166-1 |
Internformat
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| 500 | |a 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 | ||
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| id | DE-604.BV042419189 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:10:40Z |
| institution | BVB |
| isbn | 9780817681661 9781461264699 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027854606 |
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| open_access_boolean | |
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| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XV, 332 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Birkhäuser Boston |
| record_format | marc |
| series2 | Progress in Mathematical Physics |
| spellingShingle | Colombo, Fabrizio Analysis of Dirac Systems and Computational Algebra Mathematics Matrix theory Differential equations, partial Mathematical physics Partial Differential Equations Linear and Multilinear Algebras, Matrix Theory Mathematical Methods in Physics Numerical and Computational Physics Mathematik Mathematische Physik Dirac-Operator (DE-588)4150118-4 gnd Clifford-Analysis (DE-588)4484012-3 gnd |
| subject_GND | (DE-588)4150118-4 (DE-588)4484012-3 |
| title | Analysis of Dirac Systems and Computational Algebra |
| title_auth | Analysis of Dirac Systems and Computational Algebra |
| title_exact_search | Analysis of Dirac Systems and Computational Algebra |
| title_full | Analysis of Dirac Systems and Computational Algebra by Fabrizio Colombo, Irene Sabadini, Franciscus Sommen, Daniele C. Struppa |
| title_fullStr | Analysis of Dirac Systems and Computational Algebra by Fabrizio Colombo, Irene Sabadini, Franciscus Sommen, Daniele C. Struppa |
| title_full_unstemmed | Analysis of Dirac Systems and Computational Algebra by Fabrizio Colombo, Irene Sabadini, Franciscus Sommen, Daniele C. Struppa |
| title_short | Analysis of Dirac Systems and Computational Algebra |
| title_sort | analysis of dirac systems and computational algebra |
| topic | Mathematics Matrix theory Differential equations, partial Mathematical physics Partial Differential Equations Linear and Multilinear Algebras, Matrix Theory Mathematical Methods in Physics Numerical and Computational Physics Mathematik Mathematische Physik Dirac-Operator (DE-588)4150118-4 gnd Clifford-Analysis (DE-588)4484012-3 gnd |
| topic_facet | Mathematics Matrix theory Differential equations, partial Mathematical physics Partial Differential Equations Linear and Multilinear Algebras, Matrix Theory Mathematical Methods in Physics Numerical and Computational Physics Mathematik Mathematische Physik Dirac-Operator Clifford-Analysis |
| url | https://doi.org/10.1007/978-0-8176-8166-1 |
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