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Home > Education > Mathematics > Analysis in Integer and Fractional Dimensions

Analysis in Integer and Fractional Dimensions

by Blei, Ron
 
 
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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 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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Title of ebook: Analysis in Integer and Fractional Dimensions
ISBN: 9780511036972
parent-ISBN: 9780521650847
Publisher: Cambridge University Press
Internet download file size: 3425 kb
Published: 07-1997
Released online for download: 07-18-1997
Author of eBook: Blei, Ron
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