TY  - BOOK
AU  - Blei, Ron
TI  - Analysis in integer and fractional dimensions
SN  - 9780521650847
U1  - 515.2433 
PY  - 2001///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Functional analysis
KW  - Harmonic analysis
KW  - Probabilities
KW  - Inequalities
KW  - Multivariate analysis
KW  - Fractional Dimensions
N1  - Includes bibliographical references and indexes
N2  - This book provides a thorough and self-contained study of interdependence and complexity in settings of functional analysis, harmonic analysis and stochastic analysis. It is primarily aimed at students with a basic background in graduate analysis. Also of interest to computer scientists, physicists, statisticians, biologists and economists. 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
ER  -