analysis in integer and fractional dimensions cambridge studies in advanced mathematics

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Analysis In Integer And Fractional Dimensions

Author : Ron Blei
ISBN : 1139427938
Genre : Mathematics
File Size : 75. 61 MB
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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.

The Grothendieck Inequality Revisited

Author : Ron Blei
ISBN : 9780821898550
Genre : Mathematics
File Size : 31. 70 MB
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The classical Grothendieck inequality is viewed as a statement about representations of functions of two variables over discrete domains by integrals of two-fold products of functions of one variable. An analogous statement is proved, concerning continuous functions of two variables over general topological domains. The main result is the construction of a continuous map $\Phi$ from $l^2(A)$ into $L^2(\Omega_A, \mathbb{P}_A)$, where $A$ is a set, $\Omega_A = \{-1,1\}^A$, and $\mathbb{P}_A$ is the uniform probability measure on $\Omega_A$.

Recent Trends In Orthogonal Polynomials And Approximation Theory

Author : Guillermo Lopez Lagomasino
ISBN : 9780821848036
Genre : Mathematics
File Size : 27. 22 MB
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This volume contains invited lectures and selected contributions from the International Workshop on Orthogonal Polynomials and Approximation Theory, held at Universidad Carlos III de Madrid on September 8-12, 2008, and which honored Guillermo Lopez Lagomasino on his 60th birthday. This book presents the state of the art in the theory of Orthogonal Polynomials and Rational Approximation with a special emphasis on their applications in random matrices, integrable systems, and numerical quadrature. New results and methods are presented in the papers as well as a careful choice of open problems, which can foster interest in research in these mathematical areas. This volume also includes a brief account of the scientific contributions by Guillermo Lopez Lagomasino.

Normal Approximations With Malliavin Calculus

Author : Ivan Nourdin
ISBN : 9781107017771
Genre : Mathematics
File Size : 41. 35 MB
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Higher Moments Of Banach Space Valued Random Variables

Author : Svante Janson
ISBN : 9781470414658
Genre : Banach spaces
File Size : 41. 65 MB
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The authors define the :th moment of a Banach space valued random variable as the expectation of its :th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space. The authors study both the projective and injective tensor products, and their relation. Moreover, in order to be general and flexible, we study three different types of expectations: Bochner integrals, Pettis integrals and Dunford integrals.

Mathematical Reviews

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ISBN : UOM:39015056640611
Genre : Mathematics
File Size : 47. 58 MB
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Forthcoming Books

Author : Rose Arny
ISBN : UOM:39015046820406
Genre : American literature
File Size : 64. 96 MB
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American Book Publishing Record

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ISBN : STANFORD:36105111052903
Genre : Books
File Size : 37. 61 MB
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Fourier Analysis And Hausdorff Dimension

Author : Pertti Mattila
ISBN : 9781107107359
Genre : Mathematics
File Size : 45. 47 MB
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Modern text examining the interplay between measure theory and Fourier analysis.

Foundations Of Ergodic Theory

Author : Marcelo Viana
ISBN : 9781316445426
Genre : Mathematics
File Size : 51. 86 MB
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Rich with examples and applications, this textbook provides a coherent and self-contained introduction to ergodic theory, suitable for a variety of one- or two-semester courses. The authors' clear and fluent exposition helps the reader to grasp quickly the most important ideas of the theory, and their use of concrete examples illustrates these ideas and puts the results into perspective. The book requires few prerequisites, with background material supplied in the appendix. The first four chapters cover elementary material suitable for undergraduate students – invariance, recurrence and ergodicity – as well as some of the main examples. The authors then gradually build up to more sophisticated topics, including correlations, equivalent systems, entropy, the variational principle and thermodynamical formalism. The 400 exercises increase in difficulty through the text and test the reader's understanding of the whole theory. Hints and solutions are provided at the end of the book.

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