Analysis in Integer and Fractional Dimensions

by Ron Blei

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 Fr?chet 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.

• Format: Hardcover
• Language: English
• ISBN: 0521650844
• ISBN13: 9780521650847
• Release Date: August 2001
• Publisher: Cambridge University Press
• Length: 580 Pages
• Weight: 1.89 lbs.
• Dimensions: 1.3" x 6.4" x 9.3"