Banach Spaces And Their Applications In Analysis

Author : Beata Randrianantoanina,Narcisse Randrianantoanina
Publisher : Walter de Gruyter
Page : 465 pages
File Size : 55,9 Mb
Release : 2011-12-22
Category : Mathematics
ISBN : 9783110918298

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Banach Spaces and their Applications in Analysis by Beata Randrianantoanina,Narcisse Randrianantoanina Pdf

In recent years there has been a surge of profound new developments in various aspects of analysis whose connecting thread is the use of Banach space methods. Indeed, many problems seemingly far from the classical geometry of Banach spaces have been solved using Banach space techniques. This volume contains papers by participants of the conference "Banach Spaces and their Applications in Analysis", held in May 2006 at Miami University in Oxford, Ohio, in honor of Nigel Kalton's 60th birthday. In addition to research articles contributed by participants, the volume includes invited expository articles by principal speakers of the conference, who are leaders in their areas. These articles present overviews of new developments in each of the conference's main areas of emphasis, namely nonlinear theory, isomorphic theory of Banach spaces including connections with combinatorics and set theory, algebraic and homological methods in Banach spaces, approximation theory and algorithms in Banach spaces. This volume also contains an expository article about the deep and broad mathematical work of Nigel Kalton, written by his long time collaborator, Gilles Godefroy. Godefroy's article, and in fact the entire volume, illustrates the power and versatility of applications of Banach space methods and underlying connections between seemingly distant areas of analysis.

Author : Albrecht Pietsch
Publisher : Springer Science & Business Media
Page : 855 pages
File Size : 41,6 Mb
Release : 2007-12-31
Category : Mathematics
ISBN : 9780817645960

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History of Banach Spaces and Linear Operators by Albrecht Pietsch Pdf

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.

Author : Fabio Botelho
Publisher : Springer
Page : 584 pages
File Size : 47,5 Mb
Release : 2014-06-12
Category : Mathematics
ISBN : 9783319060743

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Functional Analysis and Applied Optimization in Banach Spaces by Fabio Botelho Pdf

​This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.

Author : Marián Fabian,Petr Habala,Petr Hájek,Vicente Montesinos,Václav Zizler
Publisher : Springer Science & Business Media
Page : 820 pages
File Size : 47,7 Mb
Release : 2011-02-04
Category : Mathematics
ISBN : 9781441975157

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Banach Space Theory by Marián Fabian,Petr Habala,Petr Hájek,Vicente Montesinos,Václav Zizler Pdf

Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikodým property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book.

Author : Tuomas Hytönen,Jan van Neerven,Mark Veraar,Lutz Weis
Publisher : Springer
Page : 614 pages
File Size : 48,6 Mb
Release : 2016-11-26
Category : Mathematics
ISBN : 9783319485201

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Analysis in Banach Spaces by Tuomas Hytönen,Jan van Neerven,Mark Veraar,Lutz Weis Pdf

The present volume develops the theory of integration in Banach spaces, martingales and UMD spaces, and culminates in a treatment of the Hilbert transform, Littlewood-Paley theory and the vector-valued Mihlin multiplier theorem. Over the past fifteen years, motivated by regularity problems in evolution equations, there has been tremendous progress in the analysis of Banach space-valued functions and processes. The contents of this extensive and powerful toolbox have been mostly scattered around in research papers and lecture notes. Collecting this diverse body of material into a unified and accessible presentation fills a gap in the existing literature. The principal audience that we have in mind consists of researchers who need and use Analysis in Banach Spaces as a tool for studying problems in partial differential equations, harmonic analysis, and stochastic analysis. Self-contained and offering complete proofs, this work is accessible to graduate students and researchers with a background in functional analysis or related areas.

Author : Petr Hájek,Michal Johanis
Publisher : Walter de Gruyter GmbH & Co KG
Page : 514 pages
File Size : 55,8 Mb
Release : 2014-10-29
Category : Mathematics
ISBN : 9783110258998

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Smooth Analysis in Banach Spaces by Petr Hájek,Michal Johanis Pdf

This book is about the subject of higher smoothness in separable real Banach spaces. It brings together several angles of view on polynomials, both in finite and infinite setting. Also a rather thorough and systematic view of the more recent results, and the authors work is given. The book revolves around two main broad questions: What is the best smoothness of a given Banach space, and its structural consequences? How large is a supply of smooth functions in the sense of approximating continuous functions in the uniform topology, i.e. how does the Stone-Weierstrass theorem generalize into infinite dimension where measure and compactness are not available? The subject of infinite dimensional real higher smoothness is treated here for the first time in full detail, therefore this book may also serve as a reference book.

Author : Charles Chidume
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 49,8 Mb
Release : 2009-03-27
Category : Mathematics
ISBN : 9781848821897

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Geometric Properties of Banach Spaces and Nonlinear Iterations by Charles Chidume Pdf

The contents of this monograph fall within the general area of nonlinear functional analysis and applications. We focus on an important topic within this area: geometric properties of Banach spaces and nonlinear iterations, a topic of intensive research e?orts, especially within the past 30 years, or so. In this theory, some geometric properties of Banach spaces play a crucial role. In the ?rst part of the monograph, we expose these geometric properties most of which are well known. As is well known, among all in?nite dim- sional Banach spaces, Hilbert spaces have the nicest geometric properties. The availability of the inner product, the fact that the proximity map or nearest point map of a real Hilbert space H onto a closed convex subset K of H is Lipschitzian with constant 1, and the following two identities 2 2 2 ||x+y|| =||x|| +2 x,y +||y|| , (?) 2 2 2 2 ||?x+(1??)y|| = ?||x|| +(1??)||y|| ??(1??)||x?y|| , (??) which hold for all x,y? H, are some of the geometric properties that char- terize inner product spaces and also make certain problems posed in Hilbert spaces more manageable than those in general Banach spaces. However, as has been rightly observed by M. Hazewinkel, “... many, and probably most, mathematical objects and models do not naturally live in Hilbert spaces”. Consequently,toextendsomeoftheHilbertspacetechniquestomoregeneral Banach spaces, analogues of the identities (?) and (??) have to be developed.

Author : Antonio J. Guirao,Vicente Montesinos,Václav Zizler
Publisher : Springer
Page : 169 pages
File Size : 48,5 Mb
Release : 2016-07-26
Category : Mathematics
ISBN : 9783319335728

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Open Problems in the Geometry and Analysis of Banach Spaces by Antonio J. Guirao,Vicente Montesinos,Václav Zizler Pdf

This is an collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces. Assuming the reader has a working familiarity with the basic results of Banach space theory, the authors focus on concepts of basic linear geometry, convexity, approximation, optimization, differentiability, renormings, weak compact generating, Schauder bases and biorthogonal systems, fixed points, topology and nonlinear geometry. The main purpose of this work is to help in convincing young researchers in Functional Analysis that the theory of Banach spaces is a fertile field of research, full of interesting open problems. Inside the Banach space area, the text should help expose young researchers to the depth and breadth of the work that remains, and to provide the perspective necessary to choose a direction for further study. Some of the problems are longstanding open problems, some are recent, some are more important and some are only local problems. Some would require new ideas, some may be resolved with only a subtle combination of known facts. Regardless of their origin or longevity, each of these problems documents the need for further research in this area.

Author : Terry J. Morrison
Publisher : John Wiley & Sons
Page : 380 pages
File Size : 46,8 Mb
Release : 2011-10-14
Category : Mathematics
ISBN : 9781118031247

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Functional Analysis by Terry J. Morrison Pdf

A powerful introduction to one of the most active areas of theoretical and applied mathematics This distinctive introduction to one of the most far-reaching and beautiful areas of mathematics focuses on Banach spaces as the milieu in which most of the fundamental concepts are presented. While occasionally using the more general topological vector space and locally convex space setting, it emphasizes the development of the reader's mathematical maturity and the ability to both understand and "do" mathematics. In so doing, Functional Analysis provides a strong springboard for further exploration on the wide range of topics the book presents, including: * Weak topologies and applications * Operators on Banach spaces * Bases in Banach spaces * Sequences, series, and geometry in Banach spaces Stressing the general techniques underlying the proofs, Functional Analysis also features many exercises for immediate clarification of points under discussion. This thoughtful, well-organized synthesis of the work of those mathematicians who created the discipline of functional analysis as we know it today also provides a rich source of research topics and reference material.

Author : Tuomas Hytönen,Jan van Neerven,Mark Veraar,Lutz Weis
Publisher : Springer
Page : 616 pages
File Size : 49,7 Mb
Release : 2018-02-14
Category : Mathematics
ISBN : 9783319698083

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Analysis in Banach Spaces by Tuomas Hytönen,Jan van Neerven,Mark Veraar,Lutz Weis Pdf

This second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and Littlewood-Paley Theory. It presents a thorough study of the fundamental randomisation techniques and the operator-theoretic aspects of the theory. The first two chapters address the relevant classical background from the theory of Banach spaces, including notions like type, cotype, K-convexity and contraction principles. In turn, the next two chapters provide a detailed treatment of the theory of R-boundedness and Banach space valued square functions developed over the last 20 years. In the last chapter, this content is applied to develop the holomorphic functional calculus of sectorial and bi-sectorial operators in Banach spaces. Given its breadth of coverage, this book will be an invaluable reference to graduate students and researchers interested in functional analysis, harmonic analysis, spectral theory, stochastic analysis, and the operator-theoretic approach to deterministic and stochastic evolution equations.

Author : Anonim
Publisher : Elsevier
Page : 1017 pages
File Size : 51,7 Mb
Release : 2001-08-15
Category : Mathematics
ISBN : 9780080532806

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Handbook of the Geometry of Banach Spaces by Anonim Pdf

The Handbook presents an overview of most aspects of modernBanach space theory and its applications. The up-to-date surveys, authored by leading research workers in the area, are written to be accessible to a wide audience. In addition to presenting the state of the art of Banach space theory, the surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory, and partial differential equations. The Handbook begins with a chapter on basic concepts in Banachspace theory which contains all the background needed for reading any other chapter in the Handbook. Each of the twenty one articles in this volume after the basic concepts chapter is devoted to one specific direction of Banach space theory or its applications. Each article contains a motivated introduction as well as an exposition of the main results, methods, and open problems in its specific direction. Most have an extensive bibliography. Many articles contain new proofs of known results as well as expositions of proofs which are hard to locate in the literature or are only outlined in the original research papers. As well as being valuable to experienced researchers in Banach space theory, the Handbook should be an outstanding source for inspiration and information to graduate students and beginning researchers. The Handbook will be useful for mathematicians who want to get an idea of the various developments in Banach space theory.

Author : Włodzimierz Odyniec,Grzegorz Lewicki
Publisher : Springer
Page : 184 pages
File Size : 54,5 Mb
Release : 1990
Category : Mathematics
ISBN : UOM:39015049292975

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Minimal Projections in Banach Spaces by Włodzimierz Odyniec,Grzegorz Lewicki Pdf

Author : Robert E. Megginson
Publisher : Springer Science & Business Media
Page : 613 pages
File Size : 40,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461206033

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An Introduction to Banach Space Theory by Robert E. Megginson Pdf

Preparing students for further study of both the classical works and current research, this is an accessible text for students who have had a course in real and complex analysis and understand the basic properties of L p spaces. It is sprinkled liberally with examples, historical notes, citations, and original sources, and over 450 exercises provide practice in the use of the results developed in the text through supplementary examples and counterexamples.

Author : Joseph Muscat
Publisher : Springer Nature
Page : 462 pages
File Size : 50,5 Mb
Release : 2024-06-26
Category : Electronic
ISBN : 9783031275371

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Functional Analysis by Joseph Muscat Pdf

Author : Jaroslav Lukeš
Publisher : Walter de Gruyter
Page : 732 pages
File Size : 49,5 Mb
Release : 2010
Category : Mathematics
ISBN : 9783110203202

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Integral Representation Theory by Jaroslav Lukeš Pdf

This monograph presents the state of the art of convexity, with an emphasis to integral representation. The exposition is focused on Choquet's theory of function spaces with a link to compact convex sets. An important feature of the book is an interplay between various mathematical subjects, such as functional analysis, measure theory, descriptive set theory, Banach spaces theory and potential theory. A substantial part of the material is of fairly recent origin and many results appear in the book form for the first time. The text is self-contained and covers a wide range of applications. From the contents: Geometry of convex sets Choquet theory of function spaces Affine functions on compact convex sets Perfect classes of functions and representation of affine functions Simplicial function spaces Choquet's theory of function cones Topologies on boundaries Several results on function spaces and compact convex sets Continuous and measurable selectors Construction of function spaces Function spaces in potential theory and Dirichlet problem Applications