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Analysis in Integer and Fractional Dimensions

Analysis in Integer and Fractional Dimensions

Hardcover

Series: Cambridge Studies in Advanced Mathematics, Book 71

General Mathematics

ISBN10: 0521650844
ISBN13: 9780521650847
Publisher: Cambridge University Press
Published: Jul 19 2001
Pages: 580
Weight: 1.89
Height: 1.30 Width: 6.40 Depth: 9.28
Language: English
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.

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General Mathematics