Analysis in Integer and Fractional Dimensions (Cambridge by Ron Blei

By Ron Blei

This booklet presents an intensive and self-contained examine of interdependence and complexity in settings of sensible research, harmonic research and stochastic research. It specializes in 'dimension' as a uncomplicated counter of levels of freedom, resulting in designated family 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 means of harmonic-analytic and stochastic measurements. issues comprise the (two-dimensional) Grothendieck inequality and its extensions to better dimensions, stochastic versions of Brownian movement, levels of randomness and Frechet measures in stochastic research. This publication is essentially aimed toward graduate scholars specialising in harmonic research, sensible research or likelihood concept. It comprises many routines and is acceptable for use as a textbook. it's also of curiosity to scientists from different disciplines, together with laptop scientists, physicists, statisticians, biologists and economists.

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