Geometrical Aspects Of Functional Analysis
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Geometric Aspects Of Functional Analysis
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Author : Bo'az Klartag
language : en
Publisher: Springer
Release Date : 2012-07-25
Geometric Aspects Of Functional Analysis written by Bo'az Klartag and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-25 with Mathematics categories.
This collection of original papers related to the Israeli GAFA seminar (on Geometric Aspects of Functional Analysis) from the years 2006 to 2011 continues the long tradition of the previous volumes, which reflect the general trends of Asymptotic Geometric Analysis, understood in a broad sense, and are a source of inspiration for new research. Most of the papers deal with various aspects of the theory, including classical topics in the geometry of convex bodies, inequalities involving volumes of such bodies or more generally, logarithmically-concave measures, valuation theory, probabilistic and isoperimetric problems in the combinatorial setting, volume distribution on high-dimensional spaces and characterization of classical constructions in Geometry and Analysis (like the Legendre and Fourier transforms, derivation and others). All the papers here are original research papers.
Geometric Aspects Of Functional Analysis
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Author : Vitali D. Milman
language : en
Publisher:
Release Date : 2014-09-01
Geometric Aspects Of Functional Analysis written by Vitali D. Milman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.
Geometric Aspects Of Functional Analysis
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Author : Bo'az Klartag
language : en
Publisher: Springer Nature
Release Date : 2020-06-20
Geometric Aspects Of Functional Analysis written by Bo'az Klartag and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-20 with Mathematics categories.
Continuing the theme of the previous volumes, these seminar notes reflect general trends in the study of Geometric Aspects of Functional Analysis, understood in a broad sense. Two classical topics represented are the Concentration of Measure Phenomenon in the Local Theory of Banach Spaces, which has recently had triumphs in Random Matrix Theory, and the Central Limit Theorem, one of the earliest examples of regularity and order in high dimensions. Central to the text is the study of the Poincaré and log-Sobolev functional inequalities, their reverses, and other inequalities, in which a crucial role is often played by convexity assumptions such as Log-Concavity. The concept and properties of Entropy form an important subject, with Bourgain's slicing problem and its variants drawing much attention. Constructions related to Convexity Theory are proposed and revisited, as well as inequalities that go beyond the Brunn–Minkowski theory. One of the major current research directions addressed is the identification of lower-dimensional structures with remarkable properties in rather arbitrary high-dimensional objects. In addition to functional analytic results, connections to Computer Science and to Differential Geometry are also discussed.
Geometric Aspects Of Functional Analysis
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Author : Bo'az Klartag
language : en
Publisher: Springer
Release Date : 2014-10-08
Geometric Aspects Of Functional Analysis written by Bo'az Klartag and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-08 with Mathematics categories.
As in the previous Seminar Notes, the current volume reflects general trends in the study of Geometric Aspects of Functional Analysis. Most of the papers deal with different aspects of Asymptotic Geometric Analysis, understood in a broad sense; many continue the study of geometric and volumetric properties of convex bodies and log-concave measures in high-dimensions and in particular the mean-norm, mean-width, metric entropy, spectral-gap, thin-shell and slicing parameters, with applications to Dvoretzky and Central-Limit-type results. The study of spectral properties of various systems, matrices, operators and potentials is another central theme in this volume. As expected, probabilistic tools play a significant role and probabilistic questions regarding Gaussian noise stability, the Gaussian Free Field and First Passage Percolation are also addressed. The historical connection to the field of Classical Convexity is also well represented with new properties and applications of mixed-volumes. The interplay between the real convex and complex pluri-subharmonic settings continues to manifest itself in several additional articles. All contributions are original research papers and were subject to the usual refereeing standards.
Geometric Aspects Of Functional Analysis
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Author : Bo'az Klartag
language : en
Publisher: Springer Nature
Release Date : 2020-07-08
Geometric Aspects Of Functional Analysis written by Bo'az Klartag and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-08 with Mathematics categories.
Continuing the theme of the previous volumes, these seminar notes reflect general trends in the study of Geometric Aspects of Functional Analysis, understood in a broad sense. Two classical topics represented are the Concentration of Measure Phenomenon in the Local Theory of Banach Spaces, which has recently had triumphs in Random Matrix Theory, and the Central Limit Theorem, one of the earliest examples of regularity and order in high dimensions. Central to the text is the study of the Poincaré and log-Sobolev functional inequalities, their reverses, and other inequalities, in which a crucial role is often played by convexity assumptions such as Log-Concavity. The concept and properties of Entropy form an important subject, with Bourgain's slicing problem and its variants drawing much attention. Constructions related to Convexity Theory are proposed and revisited, as well as inequalities that go beyond the Brunn–Minkowski theory. One of the major current research directions addressed is the identification of lower-dimensional structures with remarkable properties in rather arbitrary high-dimensional objects. In addition to functional analytic results, connections to Computer Science and to Differential Geometry are also discussed.
Geometrical Aspects Of Functional Analysis
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Author : Joram Lindenstrauss
language : en
Publisher: Springer
Release Date : 2006-11-15
Geometrical Aspects Of Functional Analysis written by Joram Lindenstrauss and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
These are the proceedings of the Israel Seminar on the Geometric Aspects of Functional Analysis (GAFA) which was held between October 1985 and June 1986. The main emphasis of the seminar was on the study of the geometry of Banach spaces and in particular the study of convex sets in and infinite-dimensional spaces. The greater part of the volume is made up of original research papers; a few of the papers are expository in nature. Together, they reflect the wide scope of the problems studied at present in the framework of the geometry of Banach spaces.
Geometric Aspects Of Functional Analysis
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Author : Joram Lindenstrauss
language : en
Publisher:
Release Date : 2014-09-01
Geometric Aspects Of Functional Analysis written by Joram Lindenstrauss and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.
Geometric Aspects Of Functional Analysis
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Author : Vitali D. Milman
language : en
Publisher: Springer
Release Date : 2004-08-30
Geometric Aspects Of Functional Analysis written by Vitali D. Milman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-30 with Mathematics categories.
The Israeli GAFA seminar (on Geometric Aspect of Functional Analysis) during the years 2002-2003 follows the long tradition of the previous volumes. It reflects the general trends of the theory. Most of the papers deal with different aspects of the Asymptotic Geometric Analysis. In addition the volume contains papers on related aspects of Probability, classical Convexity and also Partial Differential Equations and Banach Algebras. There are also two expository papers on topics which proved to be very much related to the main topic of the seminar. One is Statistical Learning Theory and the other is Models of Statistical Physics. All the papers of this collection are original research papers.
Geometric Functional Analysis And Its Applications
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Author : R. B. Holmes
language : en
Publisher: Springer
Release Date : 2012-12-12
Geometric Functional Analysis And Its Applications written by R. B. Holmes and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-12 with Mathematics categories.
This book has evolved from my experience over the past decade in teaching and doing research in functional analysis and certain of its appli cations. These applications are to optimization theory in general and to best approximation theory in particular. The geometric nature of the subjects has greatly influenced the approach to functional analysis presented herein, especially its basis on the unifying concept of convexity. Most of the major theorems either concern or depend on properties of convex sets; the others generally pertain to conjugate spaces or compactness properties, both of which topics are important for the proper setting and resolution of optimization problems. In consequence, and in contrast to most other treatments of functional analysis, there is no discussion of spectral theory, and only the most basic and general properties of linear operators are established. Some of the theoretical highlights of the book are the Banach space theorems associated with the names of Dixmier, Krein, James, Smulian, Bishop-Phelps, Brondsted-Rockafellar, and Bessaga-Pelczynski. Prior to these (and others) we establish to two most important principles of geometric functional analysis: the extended Krein-Milman theorem and the Hahn Banach principle, the latter appearing in ten different but equivalent formula tions (some of which are optimality criteria for convex programs). In addition, a good deal of attention is paid to properties and characterizations of conjugate spaces, especially reflexive spaces.