Analysis in Integer and Fractional Dimensions
$205.00 (C)
Part of Cambridge Studies in Advanced Mathematics
- Author: Ron Blei, University of Connecticut
- Date Published: August 2001
- availability: Available
- format: Hardback
- isbn: 9780521650847
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205.00
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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 Fréchet 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.
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×Product details
- Date Published: August 2001
- format: Hardback
- isbn: 9780521650847
- length: 580 pages
- dimensions: 236 x 160 x 33 mm
- weight: 0.885kg
- contains: 275 exercises
- availability: Available
Table of Contents
Preface
1. A prologue: mostly historical
2. Three classical inequalities
3. A fourth inequality
4. Elementary properties of the Frechet variation - an introduction to tensor products
5. The Grothendieck factorization theorem
6. An introduction to multidimensional measure theory
7. An introduction to harmonic analysis
8. Multilinear extensions of the Grothendieck inequality
9. Product Frechet measures
10. Brownian motion and the Wiener process
11. Integrator
12. A '3/2n- dimensional' Cartesian product
13. Fractional Cartesian products and combinatorial dimension
14. The last chapter: leads and loose ends.
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