Conditional Banach Spaces
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Series In Banach Spaces
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Author : Vladimir Kadets
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Series In Banach Spaces written by Vladimir Kadets and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Series of scalars, vectors, or functions are among the fundamental objects of mathematical analysis. When the arrangement of the terms is fixed, investigating a series amounts to investigating the sequence of its partial sums. In this case the theory of series is a part of the theory of sequences, which deals with their convergence, asymptotic behavior, etc. The specific character of the theory of series manifests itself when one considers rearrangements (permutations) of the terms of a series, which brings combinatorial considerations into the problems studied. The phenomenon that a numerical series can change its sum when the order of its terms is changed is one of the most impressive facts encountered in a university analysis course. The present book is devoted precisely to this aspect of the theory of series whose terms are elements of Banach (as well as other topological linear) spaces. The exposition focuses on two complementary problems. The first is to char acterize those series in a given space that remain convergent (and have the same sum) for any rearrangement of their terms; such series are usually called uncon ditionally convergent. The second problem is, when a series converges only for certain rearrangements of its terms (in other words, converges conditionally), to describe its sum range, i.e., the set of sums of all its convergent rearrangements.
Conditional Banach Spaces
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Author : Nguyen-Xuan-Loc
language : en
Publisher:
Release Date : 1969
Conditional Banach Spaces written by Nguyen-Xuan-Loc and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Banach spaces categories.
Analysis In Banach Spaces
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Author : Tuomas Hytönen
language : en
Publisher: Springer
Release Date : 2016-11-26
Analysis In Banach Spaces written by Tuomas Hytönen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-26 with Mathematics categories.
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.
Classical Banach Spaces
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Author : Joram Lindenstrauss
language : en
Publisher: Springer Science & Business Media
Release Date : 1977
Classical Banach Spaces written by Joram Lindenstrauss and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Banach spaces categories.
Probability In Banach Spaces 9
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Author : Jorgen Hoffmann-Jorgensen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Probability In Banach Spaces 9 written by Jorgen Hoffmann-Jorgensen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The papers contained in this volume are an indication of the topics th discussed and the interests of the participants of The 9 International Conference on Probability in Banach Spaces, held at Sandjberg, Denmark, August 16-21, 1993. A glance at the table of contents indicates the broad range of topics covered at this conference. What defines research in this field is not so much the topics considered but the generality of the ques tions that are asked. The goal is to examine the behavior of large classes of stochastic processes and to describe it in terms of a few simple prop erties that the processes share. The reward of research like this is that occasionally one can gain deep insight, even about familiar processes, by stripping away details, that in hindsight turn out to be extraneous. A good understanding about the disciplines involved in this field can be obtained from the recent book, Probability in Banach Spaces, Springer-Verlag, by M. Ledoux and M. Thlagrand. On page 5, of this book, there is a list of previous conferences in probability in Banach spaces, including the other eight international conferences. One can see that research in this field over the last twenty years has contributed significantly to knowledge in probability and has had important applications in many other branches of mathematics, most notably in statistics and functional analysis.
Geometry Of Banach Spaces
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Author :
language : en
Publisher: Cambridge University Press
Release Date : 1990
Geometry Of Banach Spaces written by and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Banach spaces categories.
Narrow Operators On Function Spaces And Vector Lattices
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Author : Mikhail Popov
language : en
Publisher: Walter de Gruyter
Release Date : 2012-12-06
Narrow Operators On Function Spaces And Vector Lattices written by Mikhail Popov and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Most classes of operators that are not isomorphic embeddings are characterized by some kind of a “smallness” condition. Narrow operators are those operators defined on function spaces that are “small” at {-1,0,1}-valued functions, e.g. compact operators are narrow. The original motivation to consider such operators came from theory of embeddings of Banach spaces, but since then they were also applied to the study of the Daugavet property and to other geometrical problems of functional analysis. The question of when a sum of two narrow operators is narrow, has led to deep developments of the theory of narrow operators, including an extension of the notion to vector lattices and investigations of connections to regular operators. Narrow operators were a subject of numerous investigations during the last 30 years. This monograph provides a comprehensive presentation putting them in context of modern theory. It gives an in depth systematic exposition of concepts related to and influenced by narrow operators, starting from basic results and building up to most recent developments. The authors include a complete bibliography and many attractive open problems.
Ramsey Methods In Analysis
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Author : Spiros A. Argyros
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Ramsey Methods In Analysis written by Spiros A. Argyros and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-30 with Mathematics categories.
This book contains two sets of notes prepared for the Advanced Course on R- sey Methods in Analysis given at the Centre de Recerca Matem` atica in January 2004, as part of its year-long research programme on Set Theory and its Appli- tions. The common goal of the two sets of notes is to help young mathematicians enter a very active area of research lying on the borderline between analysis and combinatorics. The solution of the distortion problem for the Hilbert space, the unconditional basic sequence problem for Banach spaces, and the Banach ho- geneous space problem are samples of the most important recent advances in this area, and our two sets of notes will give some account of this. But our main goal was to try to expose the general principles and methods that lie hidden behind and are most likely useful for further developments. The goal of the ?rst set of notes is to describe a general method of building norms with desired properties, a method that is clearly relevant when testing any sort of intuition about the in?nite-dimensional geometry of Banach spaces. The goal of the second set of notes is to expose Ramsey-theoretic methods relevant for describing the rough structure present in this sort of geometry. We would like to thank the coordinator of the Advanced Course, Joan Ba- ria, and the director of the CRM, Manuel Castellet, for giving us this challenging but rewarding opportunity. Part A SaturatedandConditional StructuresinBanachSpaces SpirosA.
Banach Spaces Harmonic Analysis And Probability Theory
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Author : R. C. Blei
language : en
Publisher: Springer
Release Date : 2006-11-15
Banach Spaces Harmonic Analysis And Probability Theory written by R. C. Blei 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.
Regularization In Banach Spaces Convergence Rates Theory
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Author : Torsten Hein
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2010
Regularization In Banach Spaces Convergence Rates Theory written by Torsten Hein and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
Motivated by their successful application in image restoring and sparsity reconstruction this manuscript deals with regularization theory of linear and nonlinear inverse and ill-posed problems in Banach space settings. Whereas regularization in Hilbert spaces has been widely studied in literature for a long period the developement and investigation of regularization methods in Banach spaces have become a field of modern research. The manuscript is twofolded. The first part deals with convergence rates theory for Tikhonov regularization as classical regularization method. In particular, generalizations of well-established results in Hilbert spaces are presented in the Banach space situation. Since the numerical effort of Tikhonov regularization in applications is rather high iterative approaches were considered as alternative regularization variants in the second part. In particular, two Gradient-type methods were presented and their behaviour concerning convergence and stability is investigated. For one of the methods, additionally, a convergence rates result is formulated. All the theoretical results are illustrated by some numerical examples.