Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs: Including a Solution to Hilbert’s Fifth Problem
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
1998
|
| Series: | Mathematics and Its Applications
452 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | This book presents a solution of the harder part of the problem of defining globally arbitrary Lie group actions on such nonsmooth entities as generalised functions. Earlier, in part 3 of Oberguggenberger & Rosinger, Lie group actions were defined globally - in the projectable case - on the nowhere dense differential algebras of generalised functions An, as well as on the Colombeau algebras of generalised functions, and also on the spaces obtained through the order completion of smooth functions, spaces which contain the solutions of arbitrary continuous nonlinear PDEs. Further details can be found in Rosinger & Rudolph, and Rosinger & Walus [1,2]. To the extent that arbitrary Lie group actions are now defined on such nonsmooth entities as generalised functions, this result can be seen as giving an ans wer to Hilbert's fifth problem, when this problem is interpreted in its original full gener ality, see for details chapter 11 |
| Physical Description: | 1 Online-Ressource (XVIII, 238 p) |
| ISBN: | 9789401590761 9789048150939 |
| DOI: | 10.1007/978-94-015-9076-1 |
Staff View
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| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401590761 9789048150939 |
| language | English |
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| spelling | Rosinger, Elemér E. Verfasser aut Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs Including a Solution to Hilbert’s Fifth Problem by Elemér E. Rosinger Dordrecht Springer Netherlands 1998 1 Online-Ressource (XVIII, 238 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 452 This book presents a solution of the harder part of the problem of defining globally arbitrary Lie group actions on such nonsmooth entities as generalised functions. Earlier, in part 3 of Oberguggenberger & Rosinger, Lie group actions were defined globally - in the projectable case - on the nowhere dense differential algebras of generalised functions An, as well as on the Colombeau algebras of generalised functions, and also on the spaces obtained through the order completion of smooth functions, spaces which contain the solutions of arbitrary continuous nonlinear PDEs. Further details can be found in Rosinger & Rudolph, and Rosinger & Walus [1,2]. To the extent that arbitrary Lie group actions are now defined on such nonsmooth entities as generalised functions, this result can be seen as giving an ans wer to Hilbert's fifth problem, when this problem is interpreted in its original full gener ality, see for details chapter 11 Mathematics Topological Groups Global analysis Differential equations, partial Partial Differential Equations Global Analysis and Analysis on Manifolds Topological Groups, Lie Groups Theoretical, Mathematical and Computational Physics Applications of Mathematics Mathematik Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 s Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s 1\p DE-604 https://doi.org/10.1007/978-94-015-9076-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Rosinger, Elemér E. Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs Including a Solution to Hilbert’s Fifth Problem Mathematics Topological Groups Global analysis Differential equations, partial Partial Differential Equations Global Analysis and Analysis on Manifolds Topological Groups, Lie Groups Theoretical, Mathematical and Computational Physics Applications of Mathematics Mathematik Lie-Gruppe (DE-588)4035695-4 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| subject_GND | (DE-588)4035695-4 (DE-588)4128900-6 |
| title | Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs Including a Solution to Hilbert’s Fifth Problem |
| title_auth | Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs Including a Solution to Hilbert’s Fifth Problem |
| title_exact_search | Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs Including a Solution to Hilbert’s Fifth Problem |
| title_full | Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs Including a Solution to Hilbert’s Fifth Problem by Elemér E. Rosinger |
| title_fullStr | Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs Including a Solution to Hilbert’s Fifth Problem by Elemér E. Rosinger |
| title_full_unstemmed | Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs Including a Solution to Hilbert’s Fifth Problem by Elemér E. Rosinger |
| title_short | Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs |
| title_sort | parametric lie group actions on global generalised solutions of nonlinear pdes including a solution to hilbert s fifth problem |
| title_sub | Including a Solution to Hilbert’s Fifth Problem |
| topic | Mathematics Topological Groups Global analysis Differential equations, partial Partial Differential Equations Global Analysis and Analysis on Manifolds Topological Groups, Lie Groups Theoretical, Mathematical and Computational Physics Applications of Mathematics Mathematik Lie-Gruppe (DE-588)4035695-4 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| topic_facet | Mathematics Topological Groups Global analysis Differential equations, partial Partial Differential Equations Global Analysis and Analysis on Manifolds Topological Groups, Lie Groups Theoretical, Mathematical and Computational Physics Applications of Mathematics Mathematik Lie-Gruppe Nichtlineare partielle Differentialgleichung |
| url | https://doi.org/10.1007/978-94-015-9076-1 |
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