Finite Sections of Some Classical Inequalities:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1970
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete
52 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Hardy, Littlewood and P6lya's famous monograph on inequalities [17J has served as an introduction to hard analysis for many mathema ticians. Some of its most interesting results center around Hilbert's inequality and generalizations. This family of inequalities determines the best bound of a family of operators on /p. When such inequalities are restricted only to finitely many variables, we can then ask for the rate at which the bounds of the restrictions approach the uniform bound. In the context of Toeplitz forms, such research was initiated over fifty years ago by Szego [37J, and the chain of ideas continues to grow strongly today, with fundamental contributions having been made by Kac, Widom, de Bruijn, and many others. In this monograph I attempt to draw together these lines of research from the point of view of sharpenings of the classical inequalities of [17]. This viewpoint leads to the exclusion of some material which might belong to a broader-based discussion, such as the elegant work of Baxter, Hirschman and others on the strong Szego limit theorem, and the inclusion of other work, such as that of de Bruijn and his students, which is basically nonlinear, and is therefore in some sense disjoint from the earlier investigations. I am grateful to Professor Halmos for inviting me to prepare this volume, and to Professors John and Olga Todd for several helpful comments. Philadelphia, Pa. H.S.W. |
| Beschreibung: | 1 Online-Ressource (VIII, 84 p) |
| ISBN: | 9783642867125 9783642867149 |
| ISSN: | 0071-1136 |
| DOI: | 10.1007/978-3-642-86712-5 |
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Datensatz im Suchindex
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| author | Wilf, Herbert S. |
| author_facet | Wilf, Herbert S. |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-86712-5 |
| format | Electronic eBook |
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| institution | BVB |
| isbn | 9783642867125 9783642867149 |
| issn | 0071-1136 |
| language | English |
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| spelling | Wilf, Herbert S. Verfasser aut Finite Sections of Some Classical Inequalities by Herbert S. Wilf Berlin, Heidelberg Springer Berlin Heidelberg 1970 1 Online-Ressource (VIII, 84 p) txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete 52 0071-1136 Hardy, Littlewood and P6lya's famous monograph on inequalities [17J has served as an introduction to hard analysis for many mathema ticians. Some of its most interesting results center around Hilbert's inequality and generalizations. This family of inequalities determines the best bound of a family of operators on /p. When such inequalities are restricted only to finitely many variables, we can then ask for the rate at which the bounds of the restrictions approach the uniform bound. In the context of Toeplitz forms, such research was initiated over fifty years ago by Szego [37J, and the chain of ideas continues to grow strongly today, with fundamental contributions having been made by Kac, Widom, de Bruijn, and many others. In this monograph I attempt to draw together these lines of research from the point of view of sharpenings of the classical inequalities of [17]. This viewpoint leads to the exclusion of some material which might belong to a broader-based discussion, such as the elegant work of Baxter, Hirschman and others on the strong Szego limit theorem, and the inclusion of other work, such as that of de Bruijn and his students, which is basically nonlinear, and is therefore in some sense disjoint from the earlier investigations. I am grateful to Professor Halmos for inviting me to prepare this volume, and to Professors John and Olga Todd for several helpful comments. Philadelphia, Pa. H.S.W. Mathematics Mathematics, general Mathematik Ungleichung (DE-588)4139098-2 gnd rswk-swf Integralgleichung (DE-588)4027229-1 gnd rswk-swf Integralungleichung (DE-588)4161917-1 gnd rswk-swf Ungleichung (DE-588)4139098-2 s 1\p DE-604 Integralgleichung (DE-588)4027229-1 s 2\p DE-604 Integralungleichung (DE-588)4161917-1 s 3\p DE-604 https://doi.org/10.1007/978-3-642-86712-5 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 | Wilf, Herbert S. Finite Sections of Some Classical Inequalities Mathematics Mathematics, general Mathematik Ungleichung (DE-588)4139098-2 gnd Integralgleichung (DE-588)4027229-1 gnd Integralungleichung (DE-588)4161917-1 gnd |
| subject_GND | (DE-588)4139098-2 (DE-588)4027229-1 (DE-588)4161917-1 |
| title | Finite Sections of Some Classical Inequalities |
| title_auth | Finite Sections of Some Classical Inequalities |
| title_exact_search | Finite Sections of Some Classical Inequalities |
| title_full | Finite Sections of Some Classical Inequalities by Herbert S. Wilf |
| title_fullStr | Finite Sections of Some Classical Inequalities by Herbert S. Wilf |
| title_full_unstemmed | Finite Sections of Some Classical Inequalities by Herbert S. Wilf |
| title_short | Finite Sections of Some Classical Inequalities |
| title_sort | finite sections of some classical inequalities |
| topic | Mathematics Mathematics, general Mathematik Ungleichung (DE-588)4139098-2 gnd Integralgleichung (DE-588)4027229-1 gnd Integralungleichung (DE-588)4161917-1 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Ungleichung Integralgleichung Integralungleichung |
| url | https://doi.org/10.1007/978-3-642-86712-5 |
| work_keys_str_mv | AT wilfherberts finitesectionsofsomeclassicalinequalities |