Analysis in integer and fractional dimensions /

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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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Blei, R. C. (Ron C.)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge ; New York : Cambridge University Press, 2001.
Colección:Cambridge studies in advanced mathematics ; 71.
Temas:
Harmonic analysis.
Functional analysis.
Probabilities.
Inequalities (Mathematics)
Fourier Analysis
Probability
Analyse harmonique.
Analyse fonctionnelle.
Probabilités.
Inégalités (Mathématiques)
probability.
MATHEMATICS > Infinity.
Functional analysis
Harmonic analysis
Probabilities
Inégalités (mathématiques)
Acceso en línea:Texto completo

MARC

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245 1 0 |a Analysis in integer and fractional dimensions /  |c Ron Blei. 
260 |a Cambridge ;  |a New York :  |b Cambridge University Press,  |c 2001. 
300 |a 1 online resource (xix, 556 pages) 
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490 1 |a Cambridge studies in advanced mathematics ;  |v 71 
504 |a Includes bibliographical references (pages 534-545) and index. 
588 0 |a Print version record. 
520 8 |a 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. 
505 0 |a Part I: A prologue: mostly historical -- Part II: Three classical inequalities -- Part III: A fourth inequality -- Part IV: Elementary properties of the Frechet variation- an introduction to tensor products -- Part V: The Grothendieck factorization theorem -- Part VI: An introduction to multidimensional measure theory -- Part VII: An introduction to harmonic analysis -- Part VIII: Multilinear extensions of the Grothendieck inequality (via "V"(2)-uniformizability) -- Part IX: Product Fréchet measures -- Part X: Brownian motion and the Wiener process -- Part XI: Integrators -- Part XII: A '3/2-dimensional' Cartesian product -- Part XIII: Fractional cartesian products and cominatorial dimension -- Part XIV: The last chapter: leads and loose ends. 
546 |a English. 
590 |a ProQuest Ebook Central  |b Ebook Central Academic Complete 
590 |a eBooks on EBSCOhost  |b EBSCO eBook Subscription Academic Collection - Worldwide 
650 0 |a Harmonic analysis. 
650 0 |a Functional analysis. 
650 0 |a Probabilities. 
650 0 |a Inequalities (Mathematics) 
650 2 |a Fourier Analysis 
650 2 |a Probability 
650 6 |a Analyse harmonique. 
650 6 |a Analyse fonctionnelle. 
650 6 |a Probabilités. 
650 6 |a Inégalités (Mathématiques) 
650 7 |a probability.  |2 aat 
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650 7 |a Functional analysis  |2 fast 
650 7 |a Harmonic analysis  |2 fast 
650 7 |a Inequalities (Mathematics)  |2 fast 
650 7 |a Probabilities  |2 fast 
650 7 |a Analyse harmonique.  |2 ram 
650 7 |a Analyse fonctionnelle.  |2 ram 
650 7 |a Probabilités.  |2 ram 
650 7 |a Inégalités (mathématiques)  |2 ram 
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776 0 8 |i Print version:  |a Blei, R.C. (Ron C.).  |t Analysis in integer and fractional dimensions.  |d Cambridge ; New York : Cambridge University Press, 2001  |w (DLC) 00064229 
830 0 |a Cambridge studies in advanced mathematics ;  |v 71. 
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