Positive Semigroups of Operators, and Applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1984
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This means that semigroup theory may be applied directly to the study of the equation I'!.f = h on M. In [45] Yau proves that, for h ~ 0, there are no nonconstant, nonnegative solutions f in [j' for 1 < p < 00. From this, Yau gets the geometric fact that complete noncom pact Riemannian manifolds with nonnegative Ricci curvature must have infinite volume, a result which was announced earlier by Calabi [4]. 6. Concluding Remarks In several of the above results, positivity of the semigroup plays an important role. This was also true, although only implicitly, for the early work of Hille and Yosida on the Fokker-Planck equation, i.e., Equation (4) with c = O. But it was Phillips [41], and Lumer and Phillips [37] who first called attention to the importance of dissipative and dispersive properties of the generator in the context of linear operators in a Banach space. The generation theorems in the Batty-Robinson paper appear to be the most definitive ones, so far, for this class of operators. The fundamental role played by the infinitesimal operator, also for the understanding of order properties, in the commutative as well as the noncommutative setting, are highlighted in a number of examples and applications in the different papers, and it is hoped that this publication will be of interest to researchers in a broad spectrum of the mathematical sub-divisions |
| Beschreibung: | 1 Online-Ressource (VI, 202 p) |
| ISBN: | 9789400964846 9789400964860 |
| DOI: | 10.1007/978-94-009-6484-6 |
Internformat
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| 500 | |a This means that semigroup theory may be applied directly to the study of the equation I'!.f = h on M. In [45] Yau proves that, for h ~ 0, there are no nonconstant, nonnegative solutions f in [j' for 1 < p < 00. From this, Yau gets the geometric fact that complete noncom pact Riemannian manifolds with nonnegative Ricci curvature must have infinite volume, a result which was announced earlier by Calabi [4]. 6. Concluding Remarks In several of the above results, positivity of the semigroup plays an important role. This was also true, although only implicitly, for the early work of Hille and Yosida on the Fokker-Planck equation, i.e., Equation (4) with c = O. But it was Phillips [41], and Lumer and Phillips [37] who first called attention to the importance of dissipative and dispersive properties of the generator in the context of linear operators in a Banach space. The generation theorems in the Batty-Robinson paper appear to be the most definitive ones, so far, for this class of operators. The fundamental role played by the infinitesimal operator, also for the understanding of order properties, in the commutative as well as the noncommutative setting, are highlighted in a number of examples and applications in the different papers, and it is hoped that this publication will be of interest to researchers in a broad spectrum of the mathematical sub-divisions | ||
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Datensatz im Suchindex
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| author | Bratteli, Ola |
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| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-search | 515 |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-009-6484-6 |
| format | Electronic eBook |
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| institution | BVB |
| isbn | 9789400964846 9789400964860 |
| language | English |
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| spelling | Bratteli, Ola Verfasser aut Positive Semigroups of Operators, and Applications edited by Ola Bratteli, Palle E. T. Jørgensen Dordrecht Springer Netherlands 1984 1 Online-Ressource (VI, 202 p) txt rdacontent c rdamedia cr rdacarrier This means that semigroup theory may be applied directly to the study of the equation I'!.f = h on M. In [45] Yau proves that, for h ~ 0, there are no nonconstant, nonnegative solutions f in [j' for 1 < p < 00. From this, Yau gets the geometric fact that complete noncom pact Riemannian manifolds with nonnegative Ricci curvature must have infinite volume, a result which was announced earlier by Calabi [4]. 6. Concluding Remarks In several of the above results, positivity of the semigroup plays an important role. This was also true, although only implicitly, for the early work of Hille and Yosida on the Fokker-Planck equation, i.e., Equation (4) with c = O. But it was Phillips [41], and Lumer and Phillips [37] who first called attention to the importance of dissipative and dispersive properties of the generator in the context of linear operators in a Banach space. The generation theorems in the Batty-Robinson paper appear to be the most definitive ones, so far, for this class of operators. The fundamental role played by the infinitesimal operator, also for the understanding of order properties, in the commutative as well as the noncommutative setting, are highlighted in a number of examples and applications in the different papers, and it is hoped that this publication will be of interest to researchers in a broad spectrum of the mathematical sub-divisions Mathematics Global analysis (Mathematics) Analysis Mathematik Positive Operatorhalbgruppe (DE-588)4175431-1 gnd rswk-swf 1\p (DE-588)4143413-4 Aufsatzsammlung gnd-content Positive Operatorhalbgruppe (DE-588)4175431-1 s 2\p DE-604 Jørgensen, Palle E. T. 1947- Sonstige (DE-588)124805515 oth https://doi.org/10.1007/978-94-009-6484-6 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 | Bratteli, Ola Positive Semigroups of Operators, and Applications Mathematics Global analysis (Mathematics) Analysis Mathematik Positive Operatorhalbgruppe (DE-588)4175431-1 gnd |
| subject_GND | (DE-588)4175431-1 (DE-588)4143413-4 |
| title | Positive Semigroups of Operators, and Applications |
| title_auth | Positive Semigroups of Operators, and Applications |
| title_exact_search | Positive Semigroups of Operators, and Applications |
| title_full | Positive Semigroups of Operators, and Applications edited by Ola Bratteli, Palle E. T. Jørgensen |
| title_fullStr | Positive Semigroups of Operators, and Applications edited by Ola Bratteli, Palle E. T. Jørgensen |
| title_full_unstemmed | Positive Semigroups of Operators, and Applications edited by Ola Bratteli, Palle E. T. Jørgensen |
| title_short | Positive Semigroups of Operators, and Applications |
| title_sort | positive semigroups of operators and applications |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Positive Operatorhalbgruppe (DE-588)4175431-1 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Positive Operatorhalbgruppe Aufsatzsammlung |
| url | https://doi.org/10.1007/978-94-009-6484-6 |
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