Analysis in Integer and Fractional Dimensions (Cambridge by Ron Blei

By Ron Blei

This ebook presents an intensive and self-contained research of interdependence and complexity in settings of sensible research, harmonic research and stochastic research. It specializes in 'dimension' as a easy counter of levels of freedom, resulting in certain kin among combinatorial measurements and numerous indices originating from the classical inequalities of Khintchin, Littlewood and Grothendieck. the fundamental techniques of fractional Cartesian items and combinatorial measurement are brought and associated with scales calibrated by way of harmonic-analytic and stochastic measurements. issues comprise the (two-dimensional) Grothendieck inequality and its extensions to raised dimensions, stochastic types of Brownian movement, levels of randomness and Frechet measures in stochastic research. This e-book is basically geared toward graduate scholars specialising in harmonic research, practical research or likelihood thought. It comprises many routines and is appropriate for use as a textbook. it's also of curiosity to scientists from different disciplines, together with machine scientists, physicists, statisticians, biologists and economists.

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