Analysis in integer and fractional dimensions /
This book provides a thorough and self-contained study of interdependence and complexity in settings of functional analysis, harmonic analysis and stochastic analysis. It focuses on 'dimension' as a basic counter of degrees of freedom, leading to precise relations between combinatorial mea...
Clasificación: | Libro Electrónico |
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Autor principal: | |
Formato: | Electrónico eBook |
Idioma: | Inglés |
Publicado: |
Cambridge ; New York :
Cambridge University Press,
2001.
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Colección: | Cambridge studies in advanced mathematics ;
71. |
Temas: | |
Acceso en línea: | Texto completo |
Sumario: | This book provides a thorough and self-contained study of interdependence and complexity in settings of functional analysis, harmonic analysis and stochastic analysis. It focuses on 'dimension' as a basic counter of degrees of freedom, leading to precise relations between combinatorial measurements and various indices originating from the classical inequalities of Khintchin, Littlewood and Grothendieck. The basic concepts of fractional Cartesian products and combinatorial dimension are introduced and linked to scales calibrated by harmonic-analytic and stochastic measurements. Topics include the (two-dimensional) Grothendieck inequality and its extensions to higher dimensions, stochastic models of Brownian motion, degrees of randomness and Frechet measures in stochastic analysis. This book is primarily aimed at graduate students specialising in harmonic analysis, functional analysis or probability theory. It contains many exercises and is suitable to be used as a textbook. It is also of interest to scientists from other disciplines, including computer scientists, physicists, statisticians, biologists and economists. |
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Descripción Física: | 1 online resource (xix, 556 pages) |
Bibliografía: | Includes bibliographical references (pages 534-545) and index. |
ISBN: | 0511012667 9780511012662 0511036973 9780511036972 9780511543012 0511543018 0521650844 9780521650847 1107117011 9781107117013 1280420561 9781280420566 9786610420568 6610420564 0511173830 9780511173837 0511153074 9780511153075 0511303343 9780511303340 0511052200 9780511052200 |