Analysis in integer and fractional dimensions /

Analysis in integer and fractional dimensions /

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Bibliographic Details
Author / Creator:Blei, R. C. (Ron C.)
Imprint:Cambridge ; New York : Cambridge University Press, 2001.
Description:1 online resource (xix, 556 pages)
Language:English
Series:Cambridge studies in advanced mathematics ; 71
Cambridge studies in advanced mathematics ; 71.
Subject:
Harmonic analysis.
Functional analysis.
Probabilities.
Inequalities (Mathematics)
Functional analysis.
Harmonic analysis.
Inequalities (Mathematics)
Probabilities.
Electronic books.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11144594
Hidden Bibliographic Details
ISBN:0511012667
9780511012662
0511036973
9780511036972
9780511543012
0511543018
0521650844
9780521650847
0521650844
9780521650847
Digital file characteristics:data file
Notes:Includes bibliographical references (pages 534-545) and index.
Print version record.
Summary: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.
Other form:Print version: Blei, R.C. (Ron C.). Analysis in integer and fractional dimensions. Cambridge ; New York : Cambridge University Press, 2001

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