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  3. Analysis in Integer and Fractional Dimensions
  • Cited by 34
Publisher:
Cambridge University Press
Online publication date:
August 2009
Print publication year:
2001
Online ISBN:
9780511543012
DOI:
https://doi.org/10.1017/CBO9780511543012
Subjects:
Mathematics (general), Mathematics, Abstract Analysis
Series:
Cambridge Studies in Advanced Mathematics (71)
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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 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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