Locally Convex Spaces and Linear Partial Differential Equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1967
|
| Schriftenreihe: | Die Grundlehren der mathematischen Wissenschaften, In Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete
146 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | It is hardly an exaggeration to say that, if the study of general topological vector spaces is justified at all, it is because of the needs of distribution and Linear PDE * theories (to which one may add the theory of convolution in spaces of hoi om orphic functions). The theorems based on TVS ** theory are generally of the "foundation" type: they will often be statements of equivalence between, say, the existence - or the approximability -of solutions to an equation Pu = v, and certain more "formal" properties of the differential operator P, for example that P be elliptic or hyperboJic, together with properties of the manifold X on which P is defined. The latter are generally geometric or topological, e. g. that X be P-convex (Definition 20. 1). Also, naturally, suitable conditions will have to be imposed upon the data, the v's, and upon the stock of possible solutions u. The effect of such theorems is to subdivide the study of an equation like Pu = v into two quite different stages. In the first stage, we shall look for the relevant equivalences, and if none is already available in the literature, we shall try to establish them. The second stage will consist of checking if the "formal" or "geometric" conditions are satisfied |
| Beschreibung: | 1 Online-Ressource (XII, 123 p) |
| ISBN: | 9783642873713 9783642873737 |
| DOI: | 10.1007/978-3-642-87371-3 |
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| 490 | 0 | |a Die Grundlehren der mathematischen Wissenschaften, In Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete |v 146 | |
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Datensatz im Suchindex
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| isbn | 9783642873713 9783642873737 |
| language | English |
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| series | Die Grundlehren der mathematischen Wissenschaften, In Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete |
| series2 | Die Grundlehren der mathematischen Wissenschaften, In Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete |
| spelling | Trèves, François 1930- Verfasser (DE-588)107758652 aut Locally Convex Spaces and Linear Partial Differential Equations by François Treves Berlin, Heidelberg Springer Berlin Heidelberg 1967 1 Online-Ressource (XII, 123 p) txt rdacontent c rdamedia cr rdacarrier Die Grundlehren der mathematischen Wissenschaften, In Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete 146 It is hardly an exaggeration to say that, if the study of general topological vector spaces is justified at all, it is because of the needs of distribution and Linear PDE * theories (to which one may add the theory of convolution in spaces of hoi om orphic functions). The theorems based on TVS ** theory are generally of the "foundation" type: they will often be statements of equivalence between, say, the existence - or the approximability -of solutions to an equation Pu = v, and certain more "formal" properties of the differential operator P, for example that P be elliptic or hyperboJic, together with properties of the manifold X on which P is defined. The latter are generally geometric or topological, e. g. that X be P-convex (Definition 20. 1). Also, naturally, suitable conditions will have to be imposed upon the data, the v's, and upon the stock of possible solutions u. The effect of such theorems is to subdivide the study of an equation like Pu = v into two quite different stages. In the first stage, we shall look for the relevant equivalences, and if none is already available in the literature, we shall try to establish them. The second stage will consist of checking if the "formal" or "geometric" conditions are satisfied Mathematics Mathematics, general Mathematik Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd rswk-swf Lokalkonvexer Raum (DE-588)4168126-5 gnd rswk-swf Lokalkonvexer Raum (DE-588)4168126-5 s Lineare partielle Differentialgleichung (DE-588)4167708-0 s 1\p DE-604 Partielle Differentialgleichung (DE-588)4044779-0 s 2\p DE-604 https://doi.org/10.1007/978-3-642-87371-3 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 | Trèves, François 1930- Locally Convex Spaces and Linear Partial Differential Equations Die Grundlehren der mathematischen Wissenschaften, In Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete Mathematics Mathematics, general Mathematik Partielle Differentialgleichung (DE-588)4044779-0 gnd Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd Lokalkonvexer Raum (DE-588)4168126-5 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4167708-0 (DE-588)4168126-5 |
| title | Locally Convex Spaces and Linear Partial Differential Equations |
| title_auth | Locally Convex Spaces and Linear Partial Differential Equations |
| title_exact_search | Locally Convex Spaces and Linear Partial Differential Equations |
| title_full | Locally Convex Spaces and Linear Partial Differential Equations by François Treves |
| title_fullStr | Locally Convex Spaces and Linear Partial Differential Equations by François Treves |
| title_full_unstemmed | Locally Convex Spaces and Linear Partial Differential Equations by François Treves |
| title_short | Locally Convex Spaces and Linear Partial Differential Equations |
| title_sort | locally convex spaces and linear partial differential equations |
| topic | Mathematics Mathematics, general Mathematik Partielle Differentialgleichung (DE-588)4044779-0 gnd Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd Lokalkonvexer Raum (DE-588)4168126-5 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Partielle Differentialgleichung Lineare partielle Differentialgleichung Lokalkonvexer Raum |
| url | https://doi.org/10.1007/978-3-642-87371-3 |
| volume_link | (DE-604)BV046778513 |
| work_keys_str_mv | AT trevesfrancois locallyconvexspacesandlinearpartialdifferentialequations |