A Nonlinear Transfer Technique For Renorming

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A Nonlinear Transfer Technique for Renorming

Aníbal Moltó
A Nonlinear Transfer Technique for Renorming Book PDF

Author : Aníbal Moltó
Publisher : Springer Science & Business Media
Page : 153 pages
File Size : 46,8 Mb
Release : 2009
Category : Mathematics
ISBN : 9783540850304

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A Nonlinear Transfer Technique for Renorming by Aníbal Moltó Pdf

Abstract topological tools from generalized metric spaces are applied in this volume to the construction of locally uniformly rotund norms on Banach spaces. The book offers new techniques for renorming problems, all of them based on a network analysis for the topologies involved inside the problem. Maps from a normed space X to a metric space Y, which provide locally uniformly rotund renormings on X, are studied and a new frame for the theory is obtained, with interplay between functional analysis, optimization and topology using subdifferentials of Lipschitz functions and covering methods of metrization theory. Any one-to-one operator T from a reflexive space X into c0 (T) satisfies the authors' conditions, transferring the norm to X. Nevertheless the authors' maps can be far from linear, for instance the duality map from X to X* gives a non-linear example when the norm in X is Fréchet differentiable. This volume will be interesting for the broad spectrum of specialists working in Banach space theory, and for researchers in infinite dimensional functional analysis.

Renormings in Banach Spaces

Antonio José Guirao,Vicente Montesinos,Václav Zizler
Renormings in Banach Spaces Book PDF

Author : Antonio José Guirao,Vicente Montesinos,Václav Zizler
Publisher : Springer Nature
Page : 621 pages
File Size : 51,5 Mb
Release : 2022-08-23
Category : Mathematics
ISBN : 9783031086557

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Renormings in Banach Spaces by Antonio José Guirao,Vicente Montesinos,Václav Zizler Pdf

This monograph presents an up-to-date panorama of the different techniques and results in the large field of renorming in Banach spaces and its applications. The reader will find a self-contained exposition of the basics on convexity and differentiability, the classical results in building equivalent norms with useful properties, and the evolution of the subject from its origin to the present days. Emphasis is done on the main ideas and their connections. The book covers several goals. First, a substantial part of it can be used as a text for graduate and other advanced courses in the geometry of Banach spaces, presenting results together with proofs, remarks and developments in a structured form. Second, a large collection of recent contributions shows the actual landscape of the field, helping the reader to access the vast existing literature, with hints of proofs and relationships among the different subtopics. Third, it can be used as a reference thanks to comprehensive lists and detailed indices that may lead to expected or unexpected information. Both specialists and newcomers to the field will find this book appealing, since its content is presented in such a way that ready-to-use results may be accessed without going into the details. This flexible approach, from the in-depth reading of a proof to the search for a useful result, together with the fact that recent results are collected here for the first time in book form, extends throughout the book. Open problems and discussions are included, encouraging the advancement of this active area of research.

Nonlinear Optimization

Immanuel M. Bomze,Vladimir F. Demyanov,Roger Fletcher,Tamás Terlaky
Nonlinear Optimization Book PDF

Author : Immanuel M. Bomze,Vladimir F. Demyanov,Roger Fletcher,Tamás Terlaky
Publisher : Springer
Page : 279 pages
File Size : 40,9 Mb
Release : 2010-03-17
Category : Mathematics
ISBN : 9783642113390

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Nonlinear Optimization by Immanuel M. Bomze,Vladimir F. Demyanov,Roger Fletcher,Tamás Terlaky Pdf

This volume collects the expanded notes of four series of lectures given on the occasion of the CIME course on Nonlinear Optimization held in Cetraro, Italy, from July 1 to 7, 2007. The Nonlinear Optimization problem of main concern here is the problem n of determining a vector of decision variables x ? R that minimizes (ma- n mizes) an objective function f(·): R ? R,when x is restricted to belong n to some feasible setF? R , usually described by a set of equality and - n n m equality constraints: F = {x ? R : h(x)=0,h(·): R ? R ; g(x) ? 0, n p g(·): R ? R }; of course it is intended that at least one of the functions f,h,g is nonlinear. Although the problem canbe stated in verysimpleterms, its solution may result very di?cult due to the analytical properties of the functions involved and/or to the number n,m,p of variables and constraints. On the other hand, the problem has been recognized to be of main relevance in engineering, economics, and other applied sciences, so that a great lot of e?ort has been devoted to develop methods and algorithms able to solve the problem even in its more di?cult and large instances. The lectures have been given by eminent scholars, who contributed to a great extent to the development of Nonlinear Optimization theory, methods and algorithms. Namely, they are: – Professor Immanuel M.

Geometry of Banach Spaces and Related Fields

Gilles Godefroy,Mohammad Sal Moslehian,Juan Benigno Seoane-Sepúlveda
Geometry of Banach Spaces and Related Fields Book PDF

Author : Gilles Godefroy,Mohammad Sal Moslehian,Juan Benigno Seoane-Sepúlveda
Publisher : American Mathematical Society
Page : 358 pages
File Size : 45,5 Mb
Release : 2024-03-27
Category : Mathematics
ISBN : 9781470475703

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Geometry of Banach Spaces and Related Fields by Gilles Godefroy,Mohammad Sal Moslehian,Juan Benigno Seoane-Sepúlveda Pdf

This book provides a comprehensive presentation of recent approaches to and results about properties of various classes of functional spaces, such as Banach spaces, uniformly convex spaces, function spaces, and Banach algebras. Each of the 12 articles in this book gives a broad overview of current subjects and presents open problems. Each article includes an extensive bibliography. This book is dedicated to Professor Per. H. Enflo, who made significant contributions to functional analysis and operator theory.

Descriptive Topology and Functional Analysis II

Juan Carlos Ferrando
Descriptive Topology and Functional Analysis II Book PDF

Author : Juan Carlos Ferrando
Publisher : Springer
Page : 298 pages
File Size : 54,8 Mb
Release : 2019-06-02
Category : Mathematics
ISBN : 9783030173760

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Descriptive Topology and Functional Analysis II by Juan Carlos Ferrando Pdf

This book is the result of a meeting on Topology and Functional Analysis, and is dedicated to Professor Manuel López-Pellicer's mathematical research. Covering topics in descriptive topology and functional analysis, including topological groups and Banach space theory, fuzzy topology, differentiability and renorming, tensor products of Banach spaces and aspects of Cp-theory, this volume is particularly useful to young researchers wanting to learn about the latest developments in these areas.

Recent Progress in General Topology III

K.P. Hart,J. van Mill,P. Simon
Recent Progress in General Topology III Book PDF

Author : K.P. Hart,J. van Mill,P. Simon
Publisher : Springer Science & Business Media
Page : 903 pages
File Size : 46,5 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9789462390249

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Recent Progress in General Topology III by K.P. Hart,J. van Mill,P. Simon Pdf

The book presents surveys describing recent developments in most of the primary subfields of General Topology, and its applications to Algebra and Analysis during the last decade, following the previous editions (North Holland, 1992 and 2002). The book was prepared in connection with the Prague Topological Symposium, held in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in 2002. The following areas experienced significant developments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems.

Methods of Contemporary Mathematical Statistical Physics

Marek Biskup,Anton Bovier,Frank den Hollander,Dima Ioffe,Fabio Martinelli,Karel Netocný,Christina Toninelli
Methods of Contemporary Mathematical Statistical Physics Book PDF

Author : Marek Biskup,Anton Bovier,Frank den Hollander,Dima Ioffe,Fabio Martinelli,Karel Netocný,Christina Toninelli
Publisher : Springer
Page : 350 pages
File Size : 40,9 Mb
Release : 2009-07-31
Category : Mathematics
ISBN : 9783540927969

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Methods of Contemporary Mathematical Statistical Physics by Marek Biskup,Anton Bovier,Frank den Hollander,Dima Ioffe,Fabio Martinelli,Karel Netocný,Christina Toninelli Pdf

This volume presents a collection of courses introducing the reader to the recent progress with attention being paid to laying solid grounds and developing various basic tools. It presents new results on phase transitions for gradient lattice models.

Advanced Courses of Mathematical Analysis V

Juan Carlos Navarro Pascual,El Amín Kaidi
Advanced Courses of Mathematical Analysis V Book PDF

Author : Juan Carlos Navarro Pascual,El Amín Kaidi
Publisher : World Scientific
Page : 320 pages
File Size : 41,8 Mb
Release : 2016-06-24
Category : Mathematics
ISBN : 9789814699709

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Advanced Courses of Mathematical Analysis V by Juan Carlos Navarro Pascual,El Amín Kaidi Pdf

This volume contains recent papers by several specialists in different fields of mathematical analysis. It offers a reasonably wide perspective of the current state of research, and new trends, in areas related to measure theory, harmonic analysis, non-associative structures in functional analysis and summability in locally convex spaces. Those interested in researching any areas of mathematical analysis will find here numerous suggestions on possible topics with an important impact today. Often, the contributions are presented in an expository nature and this makes the discussed topics accessible to a more general audience. Contents:Measurability and Semi-Continuity of Multifunctions (B Cascales)Introduction to Interpolation Theory (F Cobos)Optimality of Function Spaces in Sobolev Embeddings (L Pick)Derivations and Projections on Jordan Triples: An introduction to Nonassociative Algebra, Continuous Cohomology, and Quantum Functional Analysis (B Russo)Weighted Inequalities and Extrapolation (J Duoandikoetxea)A Note on the Off-Diagonal Muckenhoupt–Wheeden Conjecture (D Cruz-Uribe, J M Martell and C Pérez)On the Interplay Between Nonlinear Partial Differential Equations and Game Theory (J D Rossi)The Radon–Nikodým Theorem for Vector Measures and Integral Representation of Operators on Banach Function Spaces (E A Sánchez Pérez)The Orlicz–Pettis Theorem for Multiplier Convergent Series (C Swartz) Readership: Graduate students in mathematics and researchers in mathematical analysis.

Banach Space Theory

Marián Fabian,Petr Habala,Petr Hájek,Vicente Montesinos,Václav Zizler
Banach Space Theory Book PDF

Author : Marián Fabian,Petr Habala,Petr Hájek,Vicente Montesinos,Václav Zizler
Publisher : Springer Science & Business Media
Page : 820 pages
File Size : 42,5 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.

Blow-up Theories for Semilinear Parabolic Equations

Bei Hu
Blow up Theories for Semilinear Parabolic Equations Book PDF

Author : Bei Hu
Publisher : Springer
Page : 127 pages
File Size : 53,7 Mb
Release : 2011-03-17
Category : Mathematics
ISBN : 9783642184604

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Blow-up Theories for Semilinear Parabolic Equations by Bei Hu Pdf

There is an enormous amount of work in the literature about the blow-up behavior of evolution equations. It is our intention to introduce the theory by emphasizing the methods while seeking to avoid massive technical computations. To reach this goal, we use the simplest equation to illustrate the methods; these methods very often apply to more general equations.

Operator-Valued Measures and Integrals for Cone-Valued Functions

Walter Roth
Operator Valued Measures and Integrals for Cone Valued Functions Book PDF

Author : Walter Roth
Publisher : Springer Science & Business Media
Page : 370 pages
File Size : 50,7 Mb
Release : 2009-02-05
Category : Mathematics
ISBN : 9783540875642

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Operator-Valued Measures and Integrals for Cone-Valued Functions by Walter Roth Pdf

Integration theory deals with extended real-valued, vector-valued, or operator-valued measures and functions, but different approaches are used for each case. This book develops a general theory of integration that simultaneously deals with all three cases.

Harmonic Analysis on Spaces of Homogeneous Type

Donggao Deng,Yongsheng Han
Harmonic Analysis on Spaces of Homogeneous Type Book PDF

Author : Donggao Deng,Yongsheng Han
Publisher : Springer
Page : 160 pages
File Size : 43,5 Mb
Release : 2008-11-21
Category : Mathematics
ISBN : 9783540887454

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Harmonic Analysis on Spaces of Homogeneous Type by Donggao Deng,Yongsheng Han Pdf

This book could have been entitled “Analysis and Geometry.” The authors are addressing the following issue: Is it possible to perform some harmonic analysis on a set? Harmonic analysis on groups has a long tradition. Here we are given a metric set X with a (positive) Borel measure ? and we would like to construct some algorithms which in the classical setting rely on the Fourier transformation. Needless to say, the Fourier transformation does not exist on an arbitrary metric set. This endeavor is not a revolution. It is a continuation of a line of research whichwasinitiated,acenturyago,withtwofundamentalpapersthatIwould like to discuss brie?y. The ?rst paper is the doctoral dissertation of Alfred Haar, which was submitted at to University of Gottingen ̈ in July 1907. At that time it was known that the Fourier series expansion of a continuous function may diverge at a given point. Haar wanted to know if this phenomenon happens for every 2 orthonormal basis of L [0,1]. He answered this question by constructing an orthonormal basis (today known as the Haar basis) with the property that the expansion (in this basis) of any continuous function uniformly converges to that function.

Topological Complexity of Smooth Random Functions

Robert Adler,Jonathan E. Taylor
Topological Complexity of Smooth Random Functions Book PDF

Author : Robert Adler,Jonathan E. Taylor
Publisher : Springer Science & Business Media
Page : 135 pages
File Size : 49,6 Mb
Release : 2011-05-18
Category : Mathematics
ISBN : 9783642195792

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Topological Complexity of Smooth Random Functions by Robert Adler,Jonathan E. Taylor Pdf

These notes, based on lectures delivered in Saint Flour, provide an easy introduction to the authors’ 2007 Springer monograph “Random Fields and Geometry.” While not as exhaustive as the full monograph, they are also less exhausting, while still covering the basic material, typically at a more intuitive and less technical level. They also cover some more recent material relating to random algebraic topology and statistical applications. The notes include an introduction to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness. This is followed by a quick review of geometry, both integral and Riemannian, with an emphasis on tube formulae, to provide the reader with the material needed to understand and use the Gaussian kinematic formula, the main result of the notes. This is followed by chapters on topological inference and random algebraic topology, both of which provide applications of the main results.

Modules Over Operads and Functors

Benoit Fresse
Modules Over Operads and Functors Book PDF

Author : Benoit Fresse
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 55,7 Mb
Release : 2009-03-26
Category : Mathematics
ISBN : 9783540890553

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Modules Over Operads and Functors by Benoit Fresse Pdf

The notion of an operad supplies both a conceptual and effective device to handle a variety of algebraic structures in various situations. Operads were introduced 40 years ago in algebraic topology in order to model the structure of iterated loop spaces. Since then, operads have been used fruitfully in many fields of mathematics and physics. This monograph begins with a review of the basis of operad theory. The main purpose is to study structures of modules over operads as a new device to model functors between categories of algebras as effectively as operads model categories of algebras.

Generalized Bessel Functions of the First Kind

Árpád Baricz
Generalized Bessel Functions of the First Kind Book PDF

Author : Árpád Baricz
Publisher : Springer
Page : 200 pages
File Size : 52,8 Mb
Release : 2010-06-17
Category : Mathematics
ISBN : 9783642122309

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Generalized Bessel Functions of the First Kind by Árpád Baricz Pdf

In this volume we study the generalized Bessel functions of the first kind by using a number of classical and new findings in complex and classical analysis. Our aim is to present interesting geometric properties and functional inequalities for these generalized Bessel functions. Moreover, we extend many known inequalities involving circular and hyperbolic functions to Bessel and modified Bessel functions.