Author : Ron Blei
Publisher : Cambridge University Press
ISBN 13 : 1139427938
Total Pages : 580 pages
Book Rating : 4.1/5 (394 download)
Book Synopsis Analysis in Integer and Fractional Dimensions by : Ron Blei
Download or read book Analysis in Integer and Fractional Dimensions written by Ron Blei and published by Cambridge University Press. This book was released on 2001-07-19 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.