Analysis in Integer and Fractional Dimensions (Hardcover)

Ron Blei

ISBN 10: 0521650844 / ISBN 13: 9780521650847

Published by Cambridge University Press, Cambridge, 2001

About this Item

Hardcover. 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. This book provides a study of interdependence and complexity in settings of functional analysis, harmonic analysis and stochastic analysis. This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

Seller Inventory # 9780521650847

Bibliographic Details

• Title: Analysis in Integer and Fractional Dimensions (Hardcover)
• Publisher: Cambridge University Press, Cambridge
• Publication Date: 2001
• Language: English
• ISBN 10: 0521650844
• ISBN 13: 9780521650847
• Binding: Hardcover
• Edition: 1st Edition
• Condition: new

About this title

Synopsis

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 Fréchet 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.

Book Description

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 book is primarily aimed at students with a basic background in graduate analysis. Also of interest to computer scientists, physicists, statisticians, biologists and economists.