Applications of Lie Algebras to Hyperbolic and Stochastic Differential Equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1999
|
| Schriftenreihe: | Mathematics and Its Applications
466 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The main part of the book is based on a one semester graduate course for students in mathematics. I have attempted to develop the theory of hyperbolic systems of differen tial equations in a systematic way, making as much use as possible ofgradient systems and their algebraic representation. However, despite the strong sim ilarities between the development of ideas here and that found in a Lie alge bras course this is not a book on Lie algebras. The order of presentation has been determined mainly by taking into account that algebraic representation and homomorphism correspondence with a full rank Lie algebra are the basic tools which require a detailed presentation. I am aware that the inclusion of the material on algebraic and homomorphism correspondence with a full rank Lie algebra is not standard in courses on the application of Lie algebras to hyperbolic equations. I think it should be. Moreover, the Lie algebraic structure plays an important role in integral representation for solutions of nonlinear control systems and stochastic differential equations yelding results that look quite different in their original setting. Finite-dimensional nonlin ear filters for stochastic differential equations and, say, decomposability of a nonlinear control system receive a common understanding in this framework |
| Beschreibung: | 1 Online-Ressource (X, 243 p) |
| ISBN: | 9789401146791 9789401059701 |
| DOI: | 10.1007/978-94-011-4679-1 |
Internformat
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Datensatz im Suchindex
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-011-4679-1 |
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| isbn | 9789401146791 9789401059701 |
| language | English |
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| spelling | Vârsan, Constantin Verfasser aut Applications of Lie Algebras to Hyperbolic and Stochastic Differential Equations by Constantin Vârsan Dordrecht Springer Netherlands 1999 1 Online-Ressource (X, 243 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 466 The main part of the book is based on a one semester graduate course for students in mathematics. I have attempted to develop the theory of hyperbolic systems of differen tial equations in a systematic way, making as much use as possible ofgradient systems and their algebraic representation. However, despite the strong sim ilarities between the development of ideas here and that found in a Lie alge bras course this is not a book on Lie algebras. The order of presentation has been determined mainly by taking into account that algebraic representation and homomorphism correspondence with a full rank Lie algebra are the basic tools which require a detailed presentation. I am aware that the inclusion of the material on algebraic and homomorphism correspondence with a full rank Lie algebra is not standard in courses on the application of Lie algebras to hyperbolic equations. I think it should be. Moreover, the Lie algebraic structure plays an important role in integral representation for solutions of nonlinear control systems and stochastic differential equations yelding results that look quite different in their original setting. Finite-dimensional nonlin ear filters for stochastic differential equations and, say, decomposability of a nonlinear control system receive a common understanding in this framework Mathematics Algebra Differential equations, partial Systems theory Distribution (Probability theory) Non-associative Rings and Algebras Probability Theory and Stochastic Processes Partial Differential Equations Systems Theory, Control Applications of Mathematics Mathematik Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 s Stochastische Differentialgleichung (DE-588)4057621-8 s 1\p DE-604 Hyperbolische Differentialgleichung (DE-588)4131213-2 s 2\p DE-604 https://doi.org/10.1007/978-94-011-4679-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Vârsan, Constantin Applications of Lie Algebras to Hyperbolic and Stochastic Differential Equations Mathematics Algebra Differential equations, partial Systems theory Distribution (Probability theory) Non-associative Rings and Algebras Probability Theory and Stochastic Processes Partial Differential Equations Systems Theory, Control Applications of Mathematics Mathematik Stochastische Differentialgleichung (DE-588)4057621-8 gnd Lie-Algebra (DE-588)4130355-6 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd |
| subject_GND | (DE-588)4057621-8 (DE-588)4130355-6 (DE-588)4131213-2 |
| title | Applications of Lie Algebras to Hyperbolic and Stochastic Differential Equations |
| title_auth | Applications of Lie Algebras to Hyperbolic and Stochastic Differential Equations |
| title_exact_search | Applications of Lie Algebras to Hyperbolic and Stochastic Differential Equations |
| title_full | Applications of Lie Algebras to Hyperbolic and Stochastic Differential Equations by Constantin Vârsan |
| title_fullStr | Applications of Lie Algebras to Hyperbolic and Stochastic Differential Equations by Constantin Vârsan |
| title_full_unstemmed | Applications of Lie Algebras to Hyperbolic and Stochastic Differential Equations by Constantin Vârsan |
| title_short | Applications of Lie Algebras to Hyperbolic and Stochastic Differential Equations |
| title_sort | applications of lie algebras to hyperbolic and stochastic differential equations |
| topic | Mathematics Algebra Differential equations, partial Systems theory Distribution (Probability theory) Non-associative Rings and Algebras Probability Theory and Stochastic Processes Partial Differential Equations Systems Theory, Control Applications of Mathematics Mathematik Stochastische Differentialgleichung (DE-588)4057621-8 gnd Lie-Algebra (DE-588)4130355-6 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd |
| topic_facet | Mathematics Algebra Differential equations, partial Systems theory Distribution (Probability theory) Non-associative Rings and Algebras Probability Theory and Stochastic Processes Partial Differential Equations Systems Theory, Control Applications of Mathematics Mathematik Stochastische Differentialgleichung Lie-Algebra Hyperbolische Differentialgleichung |
| url | https://doi.org/10.1007/978-94-011-4679-1 |
| work_keys_str_mv | AT varsanconstantin applicationsofliealgebrastohyperbolicandstochasticdifferentialequations |