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Cover: 9780521699730 | Inequalities | A Journey into Linear Analysis | D. J. H. Garling
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Inequalities
A Journey into Linear Analysis
Taschenbuch von D. J. H. Garling
Sprache: Englisch

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Beschreibung
Contains a wealth of inequalities used in linear analysis, and explains in detail how they are used. The book begins with Cauchy's inequality and ends with Grothendieck's inequality, in between one finds the Loomis-Whitney inequality, maximal inequalities, inequalities of Hardy and of Hilbert, hypercontractive and logarithmic Sobolev inequalities, Beckner's inequality, and many, many more. The inequalities are used to obtain properties of function spaces, linear operators between them, and of special classes of operators such as absolutely summing operators. This textbook complements and fills out standard treatments, providing many diverse applications: for example, the Lebesgue decomposition theorem and the Lebesgue density theorem, the Hilbert transform and other singular integral operators, the martingale convergence theorem, eigenvalue distributions, Lidskii's trace formula, Mercer's theorem and Littlewood's 4/3 theorem. It will broaden the knowledge of postgraduate and research students, and should also appeal to their teachers, and all who work in linear analysis.
Contains a wealth of inequalities used in linear analysis, and explains in detail how they are used. The book begins with Cauchy's inequality and ends with Grothendieck's inequality, in between one finds the Loomis-Whitney inequality, maximal inequalities, inequalities of Hardy and of Hilbert, hypercontractive and logarithmic Sobolev inequalities, Beckner's inequality, and many, many more. The inequalities are used to obtain properties of function spaces, linear operators between them, and of special classes of operators such as absolutely summing operators. This textbook complements and fills out standard treatments, providing many diverse applications: for example, the Lebesgue decomposition theorem and the Lebesgue density theorem, the Hilbert transform and other singular integral operators, the martingale convergence theorem, eigenvalue distributions, Lidskii's trace formula, Mercer's theorem and Littlewood's 4/3 theorem. It will broaden the knowledge of postgraduate and research students, and should also appeal to their teachers, and all who work in linear analysis.
Über den Autor
D. J. H. Garling is an Emeritus Reader in Mathematical Analysis at the University of Cambridge and a Fellow of St John's College, Cambridge.
Zusammenfassung
Contains a wealth of inequalities used in linear analysis, and explains in detail how they are used. Properties of function spaces and linear operators between them are studied and special classes of operators, such as absolutely summing operators, are considered. This textbook complements and fills out standard treatments, providing many diverse applications. It will broaden the knowledge of postgraduate and research students, and should also appeal to their teachers, and all who work in linear analysis.
Inhaltsverzeichnis
Introduction; 1. Measure and integral; 2. The Cauchy-Schwarz inequality; 3. The AM-GM inequality; 4. Convexity, and Jensen's inequality; 5. The Lp spaces; 6. Banach function spaces; 7. Rearrangements; 8. Maximal inequalities; 9. Complex interpolation; 10. Real interpolation; 11. The Hilbert transform, and Hilbert's inequalities; 12. Khintchine's inequality; 13. Hypercontractive and logarithmic Sobolev inequalities; 14. Hadamard's inequality; 15. Hilbert space operator inequalities; 16. Summing operators; 17. Approximation numbers and eigenvalues; 18. Grothendieck's inequality, type and cotype.
Details
Erscheinungsjahr: 2014
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 346
ISBN-13: 9780521699730
ISBN-10: 0521699738
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Garling, D. J. H.
Hersteller: Cambridge University Press
Maße: 244 x 170 x 19 mm
Von/Mit: D. J. H. Garling
Erscheinungsdatum: 25.03.2014
Gewicht: 0,598 kg
preigu-id: 101959125
Über den Autor
D. J. H. Garling is an Emeritus Reader in Mathematical Analysis at the University of Cambridge and a Fellow of St John's College, Cambridge.
Zusammenfassung
Contains a wealth of inequalities used in linear analysis, and explains in detail how they are used. Properties of function spaces and linear operators between them are studied and special classes of operators, such as absolutely summing operators, are considered. This textbook complements and fills out standard treatments, providing many diverse applications. It will broaden the knowledge of postgraduate and research students, and should also appeal to their teachers, and all who work in linear analysis.
Inhaltsverzeichnis
Introduction; 1. Measure and integral; 2. The Cauchy-Schwarz inequality; 3. The AM-GM inequality; 4. Convexity, and Jensen's inequality; 5. The Lp spaces; 6. Banach function spaces; 7. Rearrangements; 8. Maximal inequalities; 9. Complex interpolation; 10. Real interpolation; 11. The Hilbert transform, and Hilbert's inequalities; 12. Khintchine's inequality; 13. Hypercontractive and logarithmic Sobolev inequalities; 14. Hadamard's inequality; 15. Hilbert space operator inequalities; 16. Summing operators; 17. Approximation numbers and eigenvalues; 18. Grothendieck's inequality, type and cotype.
Details
Erscheinungsjahr: 2014
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 346
ISBN-13: 9780521699730
ISBN-10: 0521699738
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Garling, D. J. H.
Hersteller: Cambridge University Press
Maße: 244 x 170 x 19 mm
Von/Mit: D. J. H. Garling
Erscheinungsdatum: 25.03.2014
Gewicht: 0,598 kg
preigu-id: 101959125
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