Analysis in integer and fractional dimensions

Ron Blei

556 pages, parution le 15/07/2001

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Résumé

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. 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 specializing in harmonic analysis, functional analysis or probability theory. It contains many exercises and is suitable as a textbook. It is also of interest to computer scientists, physicists, statisticians, biologists and economists.

Contents

Preface
Acknowledgements
A prologue : Mostly historical
Three classical inequalities
A fourth Inequality
Elementary properties of the Fréchet variation - an introduction to tensor products
The Grothendieck factorization theorem
An introduction to multidimensional measure theory
An introduction to harmonic analysis
Multilinear extensions of the grothendieck inequality
Product Fréchet measures
Brownian motion and the wiener process
Integrators
A 3/2-dimensional cartesian product
Fractinal cartesian products and combinatorial dimension
The last chapter : Leads and loose ends
References
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Ron Blei
Parution	15/07/2001
Nb. de pages	556
Format	15,5 x 23,5
Couverture	Relié
Poids	880g
Intérieur	Noir et Blanc
EAN13	9780521650847
ISBN13	978-0-521-65084-7