Asymptotic Theory Of Finite Dimensional Normed Spaces

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Asymptotic Theory of Finite Dimensional Normed Spaces

Author : Vitali D. Milman
Publisher : Springer
ISBN 13 : 3540388222
Total Pages : 166 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Asymptotic Theory of Finite Dimensional Normed Spaces by : Vitali D. Milman

Download or read book Asymptotic Theory of Finite Dimensional Normed Spaces written by Vitali D. Milman and published by Springer. This book was released on 2009-02-27 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the geometrical structure of finite dimensional normed spaces, as the dimension grows to infinity. This is a part of what came to be known as the Local Theory of Banach Spaces (this name was derived from the fact that in its first stages, this theory dealt mainly with relating the structure of infinite dimensional Banach spaces to the structure of their lattice of finite dimensional subspaces). Our purpose in this book is to introduce the reader to some of the results, problems, and mainly methods developed in the Local Theory, in the last few years. This by no means is a complete survey of this wide area. Some of the main topics we do not discuss here are mentioned in the Notes and Remarks section. Several books appeared recently or are going to appear shortly, which cover much of the material not covered in this book. Among these are Pisier's [Pis6] where factorization theorems related to Grothendieck's theorem are extensively discussed, and Tomczak-Jaegermann's [T-Jl] where operator ideals and distances between finite dimensional normed spaces are studied in detail. Another related book is Pietch's [Pie].

Asymptotic Theory of Finite Dimensional Normed Spaces

Author : Vitali D. Milman
Publisher :
ISBN 13 : 9783662184769
Total Pages : 172 pages
Book Rating : 4.1/5 (847 download)

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Book Synopsis Asymptotic Theory of Finite Dimensional Normed Spaces by : Vitali D. Milman

Download or read book Asymptotic Theory of Finite Dimensional Normed Spaces written by Vitali D. Milman and published by . This book was released on 2014-01-15 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Asymptotic Geometric Analysis, Part I

Author : Shiri Artstein-Avidan
Publisher : American Mathematical Soc.
ISBN 13 : 1470421933
Total Pages : 473 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Asymptotic Geometric Analysis, Part I by : Shiri Artstein-Avidan

Download or read book Asymptotic Geometric Analysis, Part I written by Shiri Artstein-Avidan and published by American Mathematical Soc.. This book was released on 2015-06-18 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomenon", one of the most powerful tools of the theory, responsible for many counterintuitive results. A central theme in this book is the interaction of randomness and pattern. At first glance, life in high dimension seems to mean the existence of multiple "possibilities", so one may expect an increase in the diversity and complexity as dimension increases. However, the concentration of measure and effects caused by convexity show that this diversity is compensated and order and patterns are created for arbitrary convex bodies in the mixture caused by high dimensionality. The book is intended for graduate students and researchers who want to learn about this exciting subject. Among the topics covered in the book are convexity, concentration phenomena, covering numbers, Dvoretzky-type theorems, volume distribution in convex bodies, and more.

Handbook of the Geometry of Banach Spaces

Author :
Publisher : Elsevier
ISBN 13 : 0080533507
Total Pages : 873 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of the Geometry of Banach Spaces by :

Download or read book Handbook of the Geometry of Banach Spaces written by and published by Elsevier. This book was released on 2003-05-06 with total page 873 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of the Geometry of Banach Spaces

Geometric Aspects of Functional Analysis

Author : Bo'az Klartag
Publisher : Springer Nature
ISBN 13 : 3030467627
Total Pages : 350 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Geometric Aspects of Functional Analysis by : Bo'az Klartag

Download or read book Geometric Aspects of Functional Analysis written by Bo'az Klartag and published by Springer Nature. This book was released on 2020-07-08 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Tsirelson's Space

Author : Peter G. Casazza
Publisher : Springer
ISBN 13 : 3540460691
Total Pages : 212 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Tsirelson's Space by : Peter G. Casazza

Download or read book Tsirelson's Space written by Peter G. Casazza and published by Springer. This book was released on 2006-11-14 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a structure theory for the increasingly important Banach space discovered by B.S. Tsirelson. The basic construction should be accessible to graduate students of functional analysis with a knowledge of the theory of Schauder bases, while topics of a more advanced nature are presented for the specialist. Bounded linear operators are studied through the use of finite-dimensional decompositions, and complemented subspaces are studied at length. A myriad of variant constructions are presented and explored, while open questions are broached in almost every chapter. Two appendices are attached: one dealing with a computer program which computes norms of finitely-supported vectors, while the other surveys recent work on weak Hilbert spaces (where a Tsirelson-type space provides an example).

Proceedings of the International Congress of Mathematicians

Author : S.D. Chatterji
Publisher : Birkhäuser
ISBN 13 : 3034890788
Total Pages : 1669 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Proceedings of the International Congress of Mathematicians by : S.D. Chatterji

Download or read book Proceedings of the International Congress of Mathematicians written by S.D. Chatterji and published by Birkhäuser. This book was released on 2012-12-06 with total page 1669 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the first ICM was held in Zürich in 1897, it has become the pinnacle of mathematical gatherings. It aims at giving an overview of the current state of different branches of mathematics and its applications as well as an insight into the treatment of special problems of exceptional importance. The proceedings of the ICMs have provided a rich chronology of mathematical development in all its branches and a unique documentation of contemporary research. They form an indispensable part of every mathematical library. The Proceedings of the International Congress of Mathematicians 1994, held in Zürich from August 3rd to 11th, 1994, are published in two volumes. Volume I contains an account of the organization of the Congress, the list of ordinary members, the reports on the work of the Fields Medalists and the Nevanlinna Prize Winner, the plenary one-hour addresses, and the invited addresses presented at Section Meetings 1 - 6. Volume II contains the invited address for Section Meetings 7 - 19. A complete author index is included in both volumes. '...the content of these impressive two volumes sheds a certain light on the present state of mathematical sciences and anybody doing research in mathematics should look carefully at these Proceedings. For young people beginning research, this is even more important, so these are a must for any serious mathematics library. The graphical presentation is, as always with Birkhäuser, excellent....' (Revue Roumaine de Mathematiques pures et Appliquées)

Visions in Mathematics

Author : Noga Alon
Publisher : Springer Science & Business Media
ISBN 13 : 3034604254
Total Pages : 539 pages
Book Rating : 4.0/5 (346 download)

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Book Synopsis Visions in Mathematics by : Noga Alon

Download or read book Visions in Mathematics written by Noga Alon and published by Springer Science & Business Media. This book was released on 2011-04-22 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Visions in Mathematics - Towards 2000" was one of the most remarkable mathematical meetings in recent years. It was held in Tel Aviv from August 25th to September 3rd, 1999, and united some of the leading mathematicians worldwide. The goals of the conference were to discuss the importance, the methods, the past and the future of mathematics as we enter the 21st century and to consider the connection between mathematics and related areas. The aims of the conference are reflected in the present set of survey articles, documenting the state of art and future prospects in many branches of mathematics of current interest. This is the second part of a two-volume set that will serve any research mathematician or advanced student as an overview and guideline through the multifaceted body of mathematical research in the present and near future.

Factorization of Linear Operators and Geometry of Banach Spaces

Author : Gilles Pisier
Publisher : American Mathematical Soc.
ISBN 13 : 9780821889053
Total Pages : 170 pages
Book Rating : 4.8/5 (89 download)

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Book Synopsis Factorization of Linear Operators and Geometry of Banach Spaces by : Gilles Pisier

Download or read book Factorization of Linear Operators and Geometry of Banach Spaces written by Gilles Pisier and published by American Mathematical Soc.. This book was released on 1986* with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:

History of Banach Spaces and Linear Operators

Author : Albrecht Pietsch
Publisher : Springer Science & Business Media
ISBN 13 : 0817645969
Total Pages : 877 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis History of Banach Spaces and Linear Operators by : Albrecht Pietsch

Download or read book History of Banach Spaces and Linear Operators written by Albrecht Pietsch and published by Springer Science & Business Media. This book was released on 2007-12-31 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.

Geometric Nonlinear Functional Analysis

Author : Yoav Benyamini
Publisher : American Mathematical Soc.
ISBN 13 : 0821808354
Total Pages : 503 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometric Nonlinear Functional Analysis by : Yoav Benyamini

Download or read book Geometric Nonlinear Functional Analysis written by Yoav Benyamini and published by American Mathematical Soc.. This book was released on 2000 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic study of geometric nonlinear functional analysis. The main theme is the study of uniformly continuous and Lipschitz functions between Banach spaces. This study leads to the classification of Banach spaces and of their important subsets in the uniform and Lipschitz categories.

Geometric Aspects of Functional Analysis

Author : Vitali D. Milman
Publisher : Springer
ISBN 13 : 3540444890
Total Pages : 299 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Geometric Aspects of Functional Analysis by : Vitali D. Milman

Download or read book Geometric Aspects of Functional Analysis written by Vitali D. Milman and published by Springer. This book was released on 2004-08-30 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Aspects of Functional Analysis

Author : V.D. Milman
Publisher : Springer
ISBN 13 : 354045392X
Total Pages : 296 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Geometric Aspects of Functional Analysis by : V.D. Milman

Download or read book Geometric Aspects of Functional Analysis written by V.D. Milman and published by Springer. This book was released on 2007-05-09 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of original research papers from the Israeli GAFA seminar during the years 1996-2000 not only reports on more traditional directions of Geometric Functional Analysis, but also reflects on some of the recent new trends in Banach Space Theory and related topics. These include the tighter connection with convexity and the resulting added emphasis on convex bodies that are not necessarily centrally symmetric, and the treatment of bodies which have only very weak convex-like structure. Another topic represented here is the use of new probabilistic tools; in particular transportation of measure methods and new inequalities emerging from Poincaré-like inequalities.

Analysis at Large

Author : Artur Avila
Publisher : Springer Nature
ISBN 13 : 3031053311
Total Pages : 388 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Analysis at Large by : Artur Avila

Download or read book Analysis at Large written by Artur Avila and published by Springer Nature. This book was released on 2022-11-01 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis at Large is dedicated to Jean Bourgain whose research has deeply influenced the mathematics discipline, particularly in analysis and its interconnections with other fields. In this volume, the contributions made by renowned experts present both research and surveys on a wide spectrum of subjects, each of which pay tribute to a true mathematical pioneer. Examples of topics discussed in this book include Bourgain’s discretized sum-product theorem, his work in nonlinear dispersive equations, the slicing problem by Bourgain, harmonious sets, the joint spectral radius, equidistribution of affine random walks, Cartan covers and doubling Bernstein type inequalities, a weighted Prékopa-Leindler inequality and sumsets with quasicubes, the fractal uncertainty principle for the Walsh-Fourier transform, the continuous formulation of shallow neural networks as Wasserstein-type gradient flows, logarithmic quantum dynamical bounds for arithmetically defined ergodic Schrödinger operators, polynomial equations in subgroups, trace sets of restricted continued fraction semigroups, exponential sums, twisted multiplicativity and moments, the ternary Goldbach problem, as well as the multiplicative group generated by two primes in Z/QZ. It is hoped that this volume will inspire further research in the areas of analysis treated in this book and also provide direction and guidance for upcoming developments in this essential subject of mathematics.

Geometric Aspects of Functional Analysis

Author : Joram Lindenstrauss
Publisher : Springer
ISBN 13 : 3540473556
Total Pages : 205 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Geometric Aspects of Functional Analysis by : Joram Lindenstrauss

Download or read book Geometric Aspects of Functional Analysis written by Joram Lindenstrauss and published by Springer. This book was released on 2006-11-14 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: The scope of the Israel seminar in geometric aspects of functional analysis during the academic year 89/90 was particularly wide covering topics as diverse as: Dynamical systems, Quantum chaos, Convex sets in Rn, Harmonic analysis and Banach space theory. The large majority of the papers are original research papers.

European Congress of Mathematics

Author : Antal Balog
Publisher : Springer Science & Business Media
ISBN 13 : 9783764354978
Total Pages : 364 pages
Book Rating : 4.3/5 (549 download)

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Book Synopsis European Congress of Mathematics by : Antal Balog

Download or read book European Congress of Mathematics written by Antal Balog and published by Springer Science & Business Media. This book was released on 1998-07-21 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of the procedings of the second European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners. Together with volume II it contains a collection of contributions by the invited lecturers. Finally, volume II also presents reports on some of the Round Table discussions. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician. Contributors: Vol. I: N. Alon, L. Ambrosio, K. Astala, R. Benedetti, Ch. Bessenrodt, F. Bethuel, P. Bjørstad, E. Bolthausen, J. Bricmont, A. Kupiainen, D. Burago, L. Caporaso, U. Dierkes, I. Dynnikov, L.H. Eliasson, W.T. Gowers, H. Hedenmalm, A. Huber, J. Kaczorowski, J. Kollár, D.O. Kramkov, A.N. Shiryaev, C. Lescop, R. März. Vol. II: J. Matousek, D. McDuff, A.S. Merkurjev, V. Milman, St. Müller, T. Nowicki, E. Olivieri, E. Scoppola, V.P. Platonov, J. Pöschel, L. Polterovich , L. Pyber, N. Simányi, J.P. Solovej, A. Stipsicz, G. Tardos, J.-P. Tignol, A.P. Veselov, E. Zuazua

High-Dimensional Probability

Author : Roman Vershynin
Publisher : Cambridge University Press
ISBN 13 : 1108244548
Total Pages : 299 pages
Book Rating : 4.1/5 (82 download)

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Book Synopsis High-Dimensional Probability by : Roman Vershynin

Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: High-dimensional probability offers insight into the behavior of random vectors, random matrices, random subspaces, and objects used to quantify uncertainty in high dimensions. Drawing on ideas from probability, analysis, and geometry, it lends itself to applications in mathematics, statistics, theoretical computer science, signal processing, optimization, and more. It is the first to integrate theory, key tools, and modern applications of high-dimensional probability. Concentration inequalities form the core, and it covers both classical results such as Hoeffding's and Chernoff's inequalities and modern developments such as the matrix Bernstein's inequality. It then introduces the powerful methods based on stochastic processes, including such tools as Slepian's, Sudakov's, and Dudley's inequalities, as well as generic chaining and bounds based on VC dimension. A broad range of illustrations is embedded throughout, including classical and modern results for covariance estimation, clustering, networks, semidefinite programming, coding, dimension reduction, matrix completion, machine learning, compressed sensing, and sparse regression.