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| Author | : Aleksander Pełczyński |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 98 |
| Release | : 1977-12-31 |
| Genre | : Mathematics |
| ISBN | : 0821816802 |
This book surveys results concerning bases and various approximation properties in the classical spaces of analytical functions. It contains extensive bibliographical comments.
| Author | : Kenneth Hoffman |
| Publisher | : Franklin Classics |
| Total Pages | : 236 |
| Release | : 2018-10-14 |
| Genre | : |
| ISBN | : 9780343131999 |
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
| Author | : Thomas H. MacGregor |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 162 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 0821842684 |
This volume is focused on Banach spaces of functions analytic in the open unit disc, such as the classical Hardy and Bergman spaces, and weighted versions of these spaces. Other spaces under consideration here include the Bloch space, the families of Cauchy transforms and fractional Cauchy transforms, BMO, VMO, and the Fock space. Some of the work deals with questions about functions in several complex variables.
| Author | : Albrecht Pietsch |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 877 |
| Release | : 2007-12-31 |
| Genre | : Mathematics |
| ISBN | : 0817645969 |
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 | : Vladimir Kadets |
| Publisher | : Birkhäuser |
| Total Pages | : 159 |
| Release | : 2011-11-11 |
| Genre | : Mathematics |
| ISBN | : 9783034899420 |
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.
| Author | : Przemysław Wojtaszczyk |
| Publisher | : Cambridge University Press |
| Total Pages | : 382 |
| Release | : 1991 |
| Genre | : Mathematics |
| ISBN | : 9780521356183 |
This book is intended to be used with graduate courses in Banach space theory.
| Author | : Graham Allan |
| Publisher | : Oxford University Press |
| Total Pages | : 380 |
| Release | : 2010-11-04 |
| Genre | : Mathematics |
| ISBN | : 0191548545 |
Banach spaces and algebras are a key topic of pure mathematics. Graham Allan's careful and detailed introductory account will prove essential reading for anyone wishing to specialise in functional analysis and is aimed at final year undergraduates or masters level students. Based on the author's lectures to fourth year students at Cambridge University, the book assumes knowledge typical of first degrees in mathematics, including metric spaces, analytic topology, and complex analysis. However, readers are not expected to be familiar with the Lebesgue theory of measure and integration. The text begins by giving the basic theory of Banach spaces, including dual spaces and bounded linear operators. It establishes forms of the theorems that are the pillars of functional analysis, including the Banach-Alaoglu, Hahn-Banach, uniform boundedness, open mapping, and closed graph theorems. There are applications to Fourier series and operators on Hilbert spaces. The main body of the text is an introduction to the theory of Banach algebras. A particular feature is the detailed account of the holomorphic functional calculus in one and several variables; all necessary background theory in one and several complex variables is fully explained, with many examples and applications considered. Throughout, exercises at sections ends help readers test their understanding, while extensive notes point to more advanced topics and sources. The book was edited for publication by Professor H. G. Dales of Leeds University, following the death of the author in August, 2007.
| Author | : Aref Jeribi |
| Publisher | : de Gruyter |
| Total Pages | : 0 |
| Release | : 2018 |
| Genre | : Mathematics |
| ISBN | : 9783110484885 |
This monograph is devoted to recent developments concerning linear operators, coveríng topics such as the Cauchy problem, Riesz basis, spectral theory and applications to the Gribov operator. Also, integral and integro-differential equations as wel
| Author | : Tuomas Hytönen |
| Publisher | : Springer Nature |
| Total Pages | : 839 |
| Release | : 2024-01-08 |
| Genre | : Mathematics |
| ISBN | : 3031465989 |
This third volume of Analysis in Banach Spaces offers a systematic treatment of Banach space-valued singular integrals, Fourier transforms, and function spaces. It further develops and ramifies the theory of functional calculus from Volume II and describes applications of these new notions and tools to the problem of maximal regularity of evolution equations. The exposition provides a unified treatment of a large body of results, much of which has previously only been available in the form of research papers. Some of the more classical topics are presented in a novel way using modern techniques amenable to a vector-valued treatment. Thanks to its accessible style with complete and detailed proofs, this book will be an invaluable reference for researchers interested in functional analysis, harmonic analysis, and the operator-theoretic approach to deterministic and stochastic evolution equations.
| Author | : Daniel Li |
| Publisher | : Cambridge University Press |
| Total Pages | : 406 |
| Release | : 2017-11-02 |
| Genre | : Mathematics |
| ISBN | : 1108300081 |
This two-volume text provides a complete overview of the theory of Banach spaces, emphasising its interplay with classical and harmonic analysis (particularly Sidon sets) and probability. The authors give a full exposition of all results, as well as numerous exercises and comments to complement the text and aid graduate students in functional analysis. The book will also be an invaluable reference volume for researchers in analysis. Volume 1 covers the basics of Banach space theory, operatory theory in Banach spaces, harmonic analysis and probability. The authors also provide an annex devoted to compact Abelian groups. Volume 2 focuses on applications of the tools presented in the first volume, including Dvoretzky's theorem, spaces without the approximation property, Gaussian processes, and more. Four leading experts also provide surveys outlining major developments in the field since the publication of the original French edition.
