Analysis in Integer and Fractional Dimensions

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This book provides a thorough and self-contained study of interdepende nce and complexity in settings of functional analysis, harmonic analys is and stochastic analysis. It focuses on "dimension" as a basic count er of degrees of freedom, leading to precise relations between combina torial measurements and various indices originating from the classical inequalities of Khintchin, Littlewood and Grothendieck. Topics includ e the (two-dimensional) Grothendieck inequality and its extensions to higher dimensions, stochastic models of Brownian motion, degrees of ra chet measures in stochastic analysis. This book is pri marily aimed at graduate students specializing in harmonic analysis, f unctional analysis or probability theory. It contains many exercises a nd is suitable as a textbook. It is also of interest to computer scien tists, physicists, statisticians, biologists and economists.

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Product Details

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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