Analysis in integer and fractional dimensions / Ron Blei.

Format:

Book

Author/Creator:

Blei, R. C. (Ron C.), author.

Series:

Cambridge studies in advanced mathematics ; 71.

Cambridge studies in advanced mathematics ; 71

Language:

English

Subjects (All):

Harmonic analysis.

Functional analysis.

Probabilities.

Inequalities (Mathematics).

Physical Description:

1 online resource (xix, 556 pages) : digital, PDF file(s).

Edition:

1st ed.

Other Title:

Analysis in Integer & Fractional Dimensions

Place of Publication:

Cambridge : Cambridge University Press, 2001.

Language Note:

English

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.

Contents:

Part I: A prologue: mostly historical

Part II: Three classical inequalities

Part III: A fourth inequality

Part IV: Elementary properties of the Frechet variation- an introduction to tensor products

Part V: The Grothendieck factorization theorem

Part VI: An introduction to multidimensional measure theory

Part VII: An introduction to harmonic analysis

Part VIII: Multilinear extensions of the Grothendieck inequality (via "V"(2)-uniformizability)

Part IX: Product Fréchet measures

Part X: Brownian motion and the Wiener process

Part XI: Integrators

Part XII: A '3/2-dimensional' Cartesian product

Part XIII: Fractional cartesian products and cominatorial dimension

Part XIV: The last chapter: leads and loose ends.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 534-545) and index.

ISBN:

1-107-11701-1

1-280-42056-1

9786610420568

0-511-17383-0

0-511-15307-4

0-511-30334-3

0-511-54301-8

0-511-05220-0

OCLC:

191035670