Analysis in integer and fractional dimensions
Material type:![Book](/opac-tmpl/lib/famfamfam/BK.png)
- 9780521650847
- 515.2433 BLE
Item type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode |
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IIT Gandhinagar General Stacks | General | 515.2433 BLE (Browse shelf(Opens below)) | 1 | Available | 030058 |
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515.2422 MUS Classical and multilinear harmonic analysis, Vol.2 | 515.243 HIR Infinite series | 515.2433 JEN Ripples in mathematics: the discrete wavelet transform | 515.2433 BLE Analysis in integer and fractional dimensions | 515.2433 BOC Harmonic analysis and the theory of probability | 515.2433 CEC Discrete harmonic analysis: representations, number theory, expanders, and the fourier transform | 515.2433 DEM Fourier restriction, decoupling, and applications |
Includes bibliographical references and indexes.
This book provides a thorough and self-contained study of interdependence and complexity in settings of functional analysis, harmonic analysis and stochastic analysis. It is primarily aimed at students with a basic background in graduate analysis. Also of interest to computer scientists, physicists, statisticians, biologists and economists. 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. The basic concepts of fractional Cartesian products and combinatorial dimension are introduced and linked to scales calibrated by harmonic-analytic and stochastic measurements. Topics include the (two-dimensional) Grothendieck inequality and its extensions to higher dimensions, stochastic models of Brownian motion, degrees of randomness and Frechet measures in stochastic analysis. This book is primarily aimed at graduate students specialising in harmonic analysis, functional analysis or probability theory. It contains many exercises and is suitable to be used as a textbook. It is also of interest to scientists from other disciplines, including computer scientists, physicists, statisticians, biologists and economists.
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