Operator Commutation Relations: Commutation Relations for Operators, Semigroups, and Resolvents with Applications to Mathematical Physics and Representations of Lie Groups
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
1984
|
| Series: | Mathematics and Its Applications
14 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | In his Retiring Presidential address, delivered before the Annual Meeting of The American Mathematical Society on December, 1948, the late Professor Einar Hille spoke on his recent results on the Lie theory of semigroups of linear transformations, . . • "So far only commutative operators have been considered and the product law . . . is the simplest possible. The non-commutative case has resisted numerous attacks in the past and it is only a few months ago that any headway was made with this problem. I shall have the pleasure of outlining the new theory here; it is a blend of the classical theory of Lie groups with the recent theory of one-parameter semigroups. " The list of references in the subsequent publication of Hille's address (Bull. Amer. Math •. Soc. 56 (1950)) includes pioneering papers of I. E. Segal, I. M. Gelfand, and K. Yosida. In the following three decades the subject grew tremendously in vitality, incorporating a number of different fields of mathematical analysis. Early papers of V. Bargmann, I. E. Segal, L. G~ding, Harish-Chandra, I. M. Singer, R. Langlands, B. Konstant, and E. Nelson developed the theoretical basis for later work in a variety of different applications: Mathematical physics, astronomy, partial differential equations, operator algebras, dynamical systems, geometry, and, most recently, stochastic filtering theory. As it turned out, of course, the Lie groups, rather than the semigroups, provided the focus of attention |
| Physical Description: | 1 Online-Ressource (XVIII, 493 p) |
| ISBN: | 9789400963283 9789400963306 |
| DOI: | 10.1007/978-94-009-6328-3 |
Staff View
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| 500 | |a In his Retiring Presidential address, delivered before the Annual Meeting of The American Mathematical Society on December, 1948, the late Professor Einar Hille spoke on his recent results on the Lie theory of semigroups of linear transformations, . . • "So far only commutative operators have been considered and the product law . . . is the simplest possible. The non-commutative case has resisted numerous attacks in the past and it is only a few months ago that any headway was made with this problem. I shall have the pleasure of outlining the new theory here; it is a blend of the classical theory of Lie groups with the recent theory of one-parameter semigroups. " The list of references in the subsequent publication of Hille's address (Bull. Amer. Math •. Soc. 56 (1950)) includes pioneering papers of I. E. Segal, I. M. Gelfand, and K. Yosida. In the following three decades the subject grew tremendously in vitality, incorporating a number of different fields of mathematical analysis. Early papers of V. Bargmann, I. E. Segal, L. G~ding, Harish-Chandra, I. M. Singer, R. Langlands, B. Konstant, and E. Nelson developed the theoretical basis for later work in a variety of different applications: Mathematical physics, astronomy, partial differential equations, operator algebras, dynamical systems, geometry, and, most recently, stochastic filtering theory. As it turned out, of course, the Lie groups, rather than the semigroups, provided the focus of attention | ||
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Record in the Search Index
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| author | Jørgensen, Palle E. T. |
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| spelling | Jørgensen, Palle E. T. Verfasser aut Operator Commutation Relations Commutation Relations for Operators, Semigroups, and Resolvents with Applications to Mathematical Physics and Representations of Lie Groups by Palle E. T. Jørgensen, Robert T. Moore Dordrecht Springer Netherlands 1984 1 Online-Ressource (XVIII, 493 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 14 In his Retiring Presidential address, delivered before the Annual Meeting of The American Mathematical Society on December, 1948, the late Professor Einar Hille spoke on his recent results on the Lie theory of semigroups of linear transformations, . . • "So far only commutative operators have been considered and the product law . . . is the simplest possible. The non-commutative case has resisted numerous attacks in the past and it is only a few months ago that any headway was made with this problem. I shall have the pleasure of outlining the new theory here; it is a blend of the classical theory of Lie groups with the recent theory of one-parameter semigroups. " The list of references in the subsequent publication of Hille's address (Bull. Amer. Math •. Soc. 56 (1950)) includes pioneering papers of I. E. Segal, I. M. Gelfand, and K. Yosida. In the following three decades the subject grew tremendously in vitality, incorporating a number of different fields of mathematical analysis. Early papers of V. Bargmann, I. E. Segal, L. G~ding, Harish-Chandra, I. M. Singer, R. Langlands, B. Konstant, and E. Nelson developed the theoretical basis for later work in a variety of different applications: Mathematical physics, astronomy, partial differential equations, operator algebras, dynamical systems, geometry, and, most recently, stochastic filtering theory. As it turned out, of course, the Lie groups, rather than the semigroups, provided the focus of attention Mathematics Global analysis (Mathematics) Analysis Mathematik Vertauschungsrelation (DE-588)4188054-7 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Differentialoperator (DE-588)4012251-7 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 s 1\p DE-604 Vertauschungsrelation (DE-588)4188054-7 s 2\p DE-604 Differentialoperator (DE-588)4012251-7 s 3\p DE-604 Lie-Gruppe (DE-588)4035695-4 s 4\p DE-604 Moore, Robert T. Sonstige oth https://doi.org/10.1007/978-94-009-6328-3 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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Jørgensen, Palle E. T. Operator Commutation Relations Commutation Relations for Operators, Semigroups, and Resolvents with Applications to Mathematical Physics and Representations of Lie Groups Mathematics Global analysis (Mathematics) Analysis Mathematik Vertauschungsrelation (DE-588)4188054-7 gnd Lie-Algebra (DE-588)4130355-6 gnd Lie-Gruppe (DE-588)4035695-4 gnd Differentialoperator (DE-588)4012251-7 gnd |
| subject_GND | (DE-588)4188054-7 (DE-588)4130355-6 (DE-588)4035695-4 (DE-588)4012251-7 |
| title | Operator Commutation Relations Commutation Relations for Operators, Semigroups, and Resolvents with Applications to Mathematical Physics and Representations of Lie Groups |
| title_auth | Operator Commutation Relations Commutation Relations for Operators, Semigroups, and Resolvents with Applications to Mathematical Physics and Representations of Lie Groups |
| title_exact_search | Operator Commutation Relations Commutation Relations for Operators, Semigroups, and Resolvents with Applications to Mathematical Physics and Representations of Lie Groups |
| title_full | Operator Commutation Relations Commutation Relations for Operators, Semigroups, and Resolvents with Applications to Mathematical Physics and Representations of Lie Groups by Palle E. T. Jørgensen, Robert T. Moore |
| title_fullStr | Operator Commutation Relations Commutation Relations for Operators, Semigroups, and Resolvents with Applications to Mathematical Physics and Representations of Lie Groups by Palle E. T. Jørgensen, Robert T. Moore |
| title_full_unstemmed | Operator Commutation Relations Commutation Relations for Operators, Semigroups, and Resolvents with Applications to Mathematical Physics and Representations of Lie Groups by Palle E. T. Jørgensen, Robert T. Moore |
| title_short | Operator Commutation Relations |
| title_sort | operator commutation relations commutation relations for operators semigroups and resolvents with applications to mathematical physics and representations of lie groups |
| title_sub | Commutation Relations for Operators, Semigroups, and Resolvents with Applications to Mathematical Physics and Representations of Lie Groups |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Vertauschungsrelation (DE-588)4188054-7 gnd Lie-Algebra (DE-588)4130355-6 gnd Lie-Gruppe (DE-588)4035695-4 gnd Differentialoperator (DE-588)4012251-7 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Vertauschungsrelation Lie-Algebra Lie-Gruppe Differentialoperator |
| url | https://doi.org/10.1007/978-94-009-6328-3 |
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