One-Parameter Semigroups for Linear Evolution Equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2000
|
| Schriftenreihe: | Graduate Texts in Mathematics
194 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The theory of one-parameter semigroups of linear operators on Banach spaces started in the first half of this century, acquired its core in 1948 with the Hille–Yosida generation theorem, and attained its first apex with the 1957 edition of Semigroups and Functional Analysis by E. Hille and R.S. Phillips. In the 1970s and 80s, thanks to the efforts of many different schools, the theory reached a certain state of perfection, which is well represented in the monographs by E.B. Davies [Dav80], J.A. Goldstein [Gol85], A. Pazy [Paz83], and others. Today, the situation is characterized by manifold applications of this theory not only to the traditional areas such as partial differential equations or stochastic processes. Semigroups have become important tools for integro-differential equations and functional differential equations, in quantum mechanics or in infinite-dimensional control theory. Semigroup methods are also applied with great success to concrete equations arising, e.g., in population dynamics or transport theory. It is quite natural, however, that semigroup theory is in competition with alternative approaches in all of these fields, and that as a whole, the relevant functional-analytic toolbox now presents a highly diversified picture. At this point we decided to write a new book, reflecting this situation but based on our personal mathematical taste. Thus, it is a book on semigroups or, more precisely, on one-parameter semigroups of bounded linear operators. In our view, this reflects the basic philosophy, first and strongly emphasized by A. Hadamard (see p. 152), that an autonomous deterministic system is described by a one-parameter semigroup of transformations |
| Beschreibung: | 1 Online-Ressource (XXI, 589 p) |
| ISBN: | 9780387226422 9780387984636 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/b97696 |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Engel, Klaus-Jochen |
| author_facet | Engel, Klaus-Jochen |
| author_role | aut |
| author_sort | Engel, Klaus-Jochen |
| author_variant | k j e kje |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/b97696 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9780387226422 9780387984636 |
| issn | 0072-5285 |
| language | English |
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| spelling | Engel, Klaus-Jochen Verfasser aut One-Parameter Semigroups for Linear Evolution Equations by Klaus-Jochen Engel, Rainer Nagel New York, NY Springer New York 2000 1 Online-Ressource (XXI, 589 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 194 0072-5285 The theory of one-parameter semigroups of linear operators on Banach spaces started in the first half of this century, acquired its core in 1948 with the Hille–Yosida generation theorem, and attained its first apex with the 1957 edition of Semigroups and Functional Analysis by E. Hille and R.S. Phillips. In the 1970s and 80s, thanks to the efforts of many different schools, the theory reached a certain state of perfection, which is well represented in the monographs by E.B. Davies [Dav80], J.A. Goldstein [Gol85], A. Pazy [Paz83], and others. Today, the situation is characterized by manifold applications of this theory not only to the traditional areas such as partial differential equations or stochastic processes. Semigroups have become important tools for integro-differential equations and functional differential equations, in quantum mechanics or in infinite-dimensional control theory. Semigroup methods are also applied with great success to concrete equations arising, e.g., in population dynamics or transport theory. It is quite natural, however, that semigroup theory is in competition with alternative approaches in all of these fields, and that as a whole, the relevant functional-analytic toolbox now presents a highly diversified picture. At this point we decided to write a new book, reflecting this situation but based on our personal mathematical taste. Thus, it is a book on semigroups or, more precisely, on one-parameter semigroups of bounded linear operators. In our view, this reflects the basic philosophy, first and strongly emphasized by A. Hadamard (see p. 152), that an autonomous deterministic system is described by a one-parameter semigroup of transformations Mathematics Global analysis (Mathematics) Analysis Mathematik Operatorhalbgruppe (DE-588)4172620-0 gnd rswk-swf Linearer Operator (DE-588)4167721-3 gnd rswk-swf Halbgruppe (DE-588)4022990-7 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 s Operatorhalbgruppe (DE-588)4172620-0 s 1\p DE-604 Linearer Operator (DE-588)4167721-3 s 2\p DE-604 Halbgruppe (DE-588)4022990-7 s 3\p DE-604 Nagel, Rainer Sonstige oth Graduate Texts in Mathematics 194 (DE-604)BV035421258 194 https://doi.org/10.1007/b97696 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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Engel, Klaus-Jochen One-Parameter Semigroups for Linear Evolution Equations Graduate Texts in Mathematics Mathematics Global analysis (Mathematics) Analysis Mathematik Operatorhalbgruppe (DE-588)4172620-0 gnd Linearer Operator (DE-588)4167721-3 gnd Halbgruppe (DE-588)4022990-7 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| subject_GND | (DE-588)4172620-0 (DE-588)4167721-3 (DE-588)4022990-7 (DE-588)4129061-6 |
| title | One-Parameter Semigroups for Linear Evolution Equations |
| title_auth | One-Parameter Semigroups for Linear Evolution Equations |
| title_exact_search | One-Parameter Semigroups for Linear Evolution Equations |
| title_full | One-Parameter Semigroups for Linear Evolution Equations by Klaus-Jochen Engel, Rainer Nagel |
| title_fullStr | One-Parameter Semigroups for Linear Evolution Equations by Klaus-Jochen Engel, Rainer Nagel |
| title_full_unstemmed | One-Parameter Semigroups for Linear Evolution Equations by Klaus-Jochen Engel, Rainer Nagel |
| title_short | One-Parameter Semigroups for Linear Evolution Equations |
| title_sort | one parameter semigroups for linear evolution equations |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Operatorhalbgruppe (DE-588)4172620-0 gnd Linearer Operator (DE-588)4167721-3 gnd Halbgruppe (DE-588)4022990-7 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Operatorhalbgruppe Linearer Operator Halbgruppe Evolutionsgleichung |
| url | https://doi.org/10.1007/b97696 |
| volume_link | (DE-604)BV035421258 |
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