Geometric Theory of Generalized Functions with Applications to General Relativity:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2001
|
| Schriftenreihe: | Mathematics and Its Applications
537 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Over the past few years a certain shift of focus within the theory of algebras of generalized functions (in the sense of J. F. Colombeau) has taken place. Originating in infinite dimensional analysis and initially applied mainly to problems in nonlinear partial differential equations involving singularities, the theory has undergone a change both in internal structure and scope of applicability, due to a growing number of applications to questions of a more geometric nature. The present book is intended to provide an in-depth presentation of these developments comprising its structural aspects within the theory of generalized functions as well as a (selective but, as we hope, representative) set of applications. This main purpose of the book is accompanied by a number of subordinate goals which we were aiming at when arranging the material included here. First, despite the fact that by now several excellent monographs on Colombeau algebras are available, we have decided to give a self-contained introduction to the field in Chapter 1. Our motivation for this decision derives from two main features of our approach. On the one hand, in contrast to other treatments of the subject we base our introduction to the field on the so-called special variant of the algebras, which makes many of the fundamental ideas of the field particularly transparent and at the same time facilitates and motivates the introduction of the more involved concepts treated later in the chapter |
| Beschreibung: | 1 Online-Ressource (XV, 505 p) |
| ISBN: | 9789401598453 9789048158805 |
| DOI: | 10.1007/978-94-015-9845-3 |
Internformat
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| 245 | 1 | 0 | |a Geometric Theory of Generalized Functions with Applications to General Relativity |c by Michael Grosser, Michael Kunzinger, Michael Oberguggenberger, Roland Steinbauer |
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| 490 | 1 | |a Mathematics and Its Applications |v 537 | |
| 500 | |a Over the past few years a certain shift of focus within the theory of algebras of generalized functions (in the sense of J. F. Colombeau) has taken place. Originating in infinite dimensional analysis and initially applied mainly to problems in nonlinear partial differential equations involving singularities, the theory has undergone a change both in internal structure and scope of applicability, due to a growing number of applications to questions of a more geometric nature. The present book is intended to provide an in-depth presentation of these developments comprising its structural aspects within the theory of generalized functions as well as a (selective but, as we hope, representative) set of applications. This main purpose of the book is accompanied by a number of subordinate goals which we were aiming at when arranging the material included here. First, despite the fact that by now several excellent monographs on Colombeau algebras are available, we have decided to give a self-contained introduction to the field in Chapter 1. Our motivation for this decision derives from two main features of our approach. On the one hand, in contrast to other treatments of the subject we base our introduction to the field on the so-called special variant of the algebras, which makes many of the fundamental ideas of the field particularly transparent and at the same time facilitates and motivates the introduction of the more involved concepts treated later in the chapter | ||
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Datensatz im Suchindex
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| author | Grosser, Michael |
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| author_sort | Grosser, Michael |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7 |
| dewey-search | 515.7 |
| dewey-sort | 3515.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-015-9845-3 |
| format | Electronic eBook |
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| id | DE-604.BV042424169 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401598453 9789048158805 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859586 |
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| physical | 1 Online-Ressource (XV, 505 p) |
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| series | Mathematics and Its Applications |
| series2 | Mathematics and Its Applications |
| spelling | Grosser, Michael Verfasser (DE-588)1294365010 aut Geometric Theory of Generalized Functions with Applications to General Relativity by Michael Grosser, Michael Kunzinger, Michael Oberguggenberger, Roland Steinbauer Dordrecht Springer Netherlands 2001 1 Online-Ressource (XV, 505 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 537 Over the past few years a certain shift of focus within the theory of algebras of generalized functions (in the sense of J. F. Colombeau) has taken place. Originating in infinite dimensional analysis and initially applied mainly to problems in nonlinear partial differential equations involving singularities, the theory has undergone a change both in internal structure and scope of applicability, due to a growing number of applications to questions of a more geometric nature. The present book is intended to provide an in-depth presentation of these developments comprising its structural aspects within the theory of generalized functions as well as a (selective but, as we hope, representative) set of applications. This main purpose of the book is accompanied by a number of subordinate goals which we were aiming at when arranging the material included here. First, despite the fact that by now several excellent monographs on Colombeau algebras are available, we have decided to give a self-contained introduction to the field in Chapter 1. Our motivation for this decision derives from two main features of our approach. On the one hand, in contrast to other treatments of the subject we base our introduction to the field on the so-called special variant of the algebras, which makes many of the fundamental ideas of the field particularly transparent and at the same time facilitates and motivates the introduction of the more involved concepts treated later in the chapter Mathematics Topological Groups Functional analysis Global analysis Functional Analysis Global Analysis and Analysis on Manifolds Applications of Mathematics Theoretical, Mathematical and Computational Physics Topological Groups, Lie Groups Mathematik Kunzinger, Michael Sonstige oth Oberguggenberger, Michael Sonstige oth Steinbauer, Roland Sonstige (DE-588)139370897 oth Mathematics and Its Applications 537 (DE-604)BV008163334 537 https://doi.org/10.1007/978-94-015-9845-3 Verlag Volltext |
| spellingShingle | Grosser, Michael Geometric Theory of Generalized Functions with Applications to General Relativity Mathematics and Its Applications Mathematics Topological Groups Functional analysis Global analysis Functional Analysis Global Analysis and Analysis on Manifolds Applications of Mathematics Theoretical, Mathematical and Computational Physics Topological Groups, Lie Groups Mathematik |
| title | Geometric Theory of Generalized Functions with Applications to General Relativity |
| title_auth | Geometric Theory of Generalized Functions with Applications to General Relativity |
| title_exact_search | Geometric Theory of Generalized Functions with Applications to General Relativity |
| title_full | Geometric Theory of Generalized Functions with Applications to General Relativity by Michael Grosser, Michael Kunzinger, Michael Oberguggenberger, Roland Steinbauer |
| title_fullStr | Geometric Theory of Generalized Functions with Applications to General Relativity by Michael Grosser, Michael Kunzinger, Michael Oberguggenberger, Roland Steinbauer |
| title_full_unstemmed | Geometric Theory of Generalized Functions with Applications to General Relativity by Michael Grosser, Michael Kunzinger, Michael Oberguggenberger, Roland Steinbauer |
| title_short | Geometric Theory of Generalized Functions with Applications to General Relativity |
| title_sort | geometric theory of generalized functions with applications to general relativity |
| topic | Mathematics Topological Groups Functional analysis Global analysis Functional Analysis Global Analysis and Analysis on Manifolds Applications of Mathematics Theoretical, Mathematical and Computational Physics Topological Groups, Lie Groups Mathematik |
| topic_facet | Mathematics Topological Groups Functional analysis Global analysis Functional Analysis Global Analysis and Analysis on Manifolds Applications of Mathematics Theoretical, Mathematical and Computational Physics Topological Groups, Lie Groups Mathematik |
| url | https://doi.org/10.1007/978-94-015-9845-3 |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT grossermichael geometrictheoryofgeneralizedfunctionswithapplicationstogeneralrelativity AT kunzingermichael geometrictheoryofgeneralizedfunctionswithapplicationstogeneralrelativity AT oberguggenbergermichael geometrictheoryofgeneralizedfunctionswithapplicationstogeneralrelativity AT steinbauerroland geometrictheoryofgeneralizedfunctionswithapplicationstogeneralrelativity |