Download Analysis in Integer and Fractional Dimensions (Cambridge by Ron Blei PDF

By Ron Blei

This publication offers an intensive and self-contained examine of interdependence and complexity in settings of useful research, harmonic research and stochastic research. It makes a speciality of 'dimension' as a uncomplicated counter of levels of freedom, resulting in distinct kin among combinatorial measurements and numerous indices originating from the classical inequalities of Khintchin, Littlewood and Grothendieck. the elemental options of fractional Cartesian items and combinatorial measurement are brought and associated with scales calibrated through harmonic-analytic and stochastic measurements. issues contain 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 aimed toward graduate scholars specialising in harmonic research, practical research or chance conception. It includes many routines and is appropriate 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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