Topological Vector Spaces

Author : François Treves
Publisher : Elsevier
Page : 582 pages
File Size : 44,9 Mb
Release : 2016-06-03
Category : Mathematics
ISBN : 9781483223629

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Topological Vector Spaces, Distributions and Kernels by François Treves Pdf

Topological Vector Spaces, Distributions and Kernels discusses partial differential equations involving spaces of functions and space distributions. The book reviews the definitions of a vector space, of a topological space, and of the completion of a topological vector space. The text gives examples of Frechet spaces, Normable spaces, Banach spaces, or Hilbert spaces. The theory of Hilbert space is similar to finite dimensional Euclidean spaces in which they are complete and carry an inner product that can determine their properties. The text also explains the Hahn-Banach theorem, as well as the applications of the Banach-Steinhaus theorem and the Hilbert spaces. The book discusses topologies compatible with a duality, the theorem of Mackey, and reflexivity. The text describes nuclear spaces, the Kernels theorem and the nuclear operators in Hilbert spaces. Kernels and topological tensor products theory can be applied to linear partial differential equations where kernels, in this connection, as inverses (or as approximations of inverses), of differential operators. The book is suitable for vector mathematicians, for students in advanced mathematics and physics.

Author : Lawrence Narici,Edward Beckenstein
Publisher : CRC Press
Page : 628 pages
File Size : 52,6 Mb
Release : 2010-07-26
Category : Mathematics
ISBN : 9781584888673

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Topological Vector Spaces by Lawrence Narici,Edward Beckenstein Pdf

With many new concrete examples and historical notes, Topological Vector Spaces, Second Edition provides one of the most thorough and up-to-date treatments of the Hahn-Banach theorem. This edition explores the theorem's connection with the axiom of choice, discusses the uniqueness of Hahn-Banach extensions, and includes an entirely new chapter on v

Author : Jürgen Voigt
Publisher : Springer Nature
Page : 152 pages
File Size : 41,5 Mb
Release : 2020-03-06
Category : Mathematics
ISBN : 9783030329457

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A Course on Topological Vector Spaces by Jürgen Voigt Pdf

This book provides an introduction to the theory of topological vector spaces, with a focus on locally convex spaces. It discusses topologies in dual pairs, culminating in the Mackey-Arens theorem, and also examines the properties of the weak topology on Banach spaces, for instance Banach’s theorem on weak*-closed subspaces on the dual of a Banach space (alias the Krein-Smulian theorem), the Eberlein-Smulian theorem, Krein’s theorem on the closed convex hull of weakly compact sets in a Banach space, and the Dunford-Pettis theorem characterising weak compactness in L1-spaces. Lastly, it addresses topics such as the locally convex final topology, with the application to test functions D(Ω) and the space of distributions, and the Krein-Milman theorem. The book adopts an “economic” approach to interesting topics, and avoids exploring all the arising side topics. Written in a concise mathematical style, it is intended primarily for advanced graduate students with a background in elementary functional analysis, but is also useful as a reference text for established mathematicians.

Author : N. Bourbaki
Publisher : Springer Science & Business Media
Page : 368 pages
File Size : 47,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642617157

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Topological Vector Spaces by N. Bourbaki Pdf

This is a softcover reprint of the 1987 English translation of the second edition of Bourbaki's Espaces Vectoriels Topologiques. Much of the material has been rearranged, rewritten, or replaced by a more up-to-date exposition, and a good deal of new material has been incorporated in this book, reflecting decades of progress in the field.

Author : Albert Wilansky
Publisher : Courier Corporation
Page : 324 pages
File Size : 43,8 Mb
Release : 2013-01-01
Category : Mathematics
ISBN : 9780486493534

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Modern Methods in Topological Vector Spaces by Albert Wilansky Pdf

"Designed for a one-year course in topological vector spaces, this text is geared toward beginning graduate students of mathematics. Topics include Banach space, open mapping and closed graph theorems, local convexity, duality, equicontinuity, operators,inductive limits, and compactness and barrelled spaces. Extensive tables cover theorems and counterexamples. Rich problem sections throughout the book. 1978 edition"--

Author : V.I. Bogachev,O.G. Smolyanov
Publisher : Springer
Page : 456 pages
File Size : 46,7 Mb
Release : 2017-05-16
Category : Mathematics
ISBN : 9783319571171

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Topological Vector Spaces and Their Applications by V.I. Bogachev,O.G. Smolyanov Pdf

This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle nature, which cannot be regarded as basic, but knowledge which is useful for understanding applications. Finally, the book explores some of such applications connected with differential calculus and measure theory in infinite-dimensional spaces. These applications are a central aspect of the book, which is why it is different from the wide range of existing texts on topological vector spaces. Overall, this book develops differential and integral calculus on infinite-dimensional locally convex spaces by using methods and techniques of the theory of locally convex spaces. The target readership includes mathematicians and physicists whose research is related to infinite-dimensional analysis.

Author : Gottfried Köthe
Publisher : Springer Science & Business Media
Page : 470 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642649882

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Topological Vector Spaces I by Gottfried Köthe Pdf

It is the author's aim to give a systematic account of the most im portant ideas, methods and results of the theory of topological vector spaces. After a rapid development during the last 15 years, this theory has now achieved a form which makes such an account seem both possible and desirable. This present first volume begins with the fundamental ideas of general topology. These are of crucial importance for the theory that follows, and so it seems necessary to give a concise account, giving complete proofs. This also has the advantage that the only preliminary knowledge required for reading this book is of classical analysis and set theory. In the second chapter, infinite dimensional linear algebra is considered in comparative detail. As a result, the concept of dual pair and linear topologies on vector spaces over arbitrary fields are intro duced in a natural way. It appears to the author to be of interest to follow the theory of these linearly topologised spaces quite far, since this theory can be developed in a way which closely resembles the theory of locally convex spaces. It should however be stressed that this part of chapter two is not needed for the comprehension of the later chapters. Chapter three is concerned with real and complex topological vector spaces. The classical results of Banach's theory are given here, as are fundamental results about convex sets in infinite dimensional spaces.

Author : John Horvath
Publisher : Courier Corporation
Page : 466 pages
File Size : 48,8 Mb
Release : 2013-10-03
Category : Mathematics
ISBN : 9780486311036

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Topological Vector Spaces and Distributions by John Horvath Pdf

Precise exposition provides an excellent summary of the modern theory of locally convex spaces and develops the theory of distributions in terms of convolutions, tensor products, and Fourier transforms. 1966 edition.

Author : Alex P. Robertson,Wendy Robertson
Publisher : CUP Archive
Page : 186 pages
File Size : 52,5 Mb
Release : 1980
Category : Mathematics
ISBN : 0521298822

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Topological Vector Spaces by Alex P. Robertson,Wendy Robertson Pdf

Author : Lucien Waelbroeck
Publisher : Springer
Page : 165 pages
File Size : 46,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540369387

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Topological Vector Spaces and Algebras by Lucien Waelbroeck Pdf

The lectures associated with these notes were given at the Instituto de Matematica Pura e Aplicada (IMPA) in Rio de Janeiro, during the local winter 1970. To emphasize the properties of topological algebras, the author had started out his lecture with results about topological algebras, and introduced the linear results as he went along.

Author : John Horvath
Publisher : Courier Corporation
Page : 466 pages
File Size : 52,5 Mb
Release : 2012-01-01
Category : Mathematics
ISBN : 9780486488509

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Topological Vector Spaces and Distributions by John Horvath Pdf

"The most readable introduction to the theory of vector spaces available in English and possibly any other language."—J. L. B. Cooper, MathSciNet ReviewMathematically rigorous but user-friendly, this classic treatise discusses major modern contributions to the field of topological vector spaces. The self-contained treatment includes complete proofs for all necessary results from algebra and topology. Suitable for undergraduate mathematics majors with a background in advanced calculus, this volume will also assist professional mathematicians, physicists, and engineers.The precise exposition of the first three chapters—covering Banach spaces, locally convex spaces, and duality—provides an excellent summary of the modern theory of locally convex spaces. The fourth and final chapter develops the theory of distributions in relation to convolutions, tensor products, and Fourier transforms. Augmented with many examples and exercises, the text includes an extensive bibliography.Reprint of the Addison-Wesley Publishing Company, Reading, Massachusetts, 1966 edition.

Author : S.M. Khaleelulla
Publisher : Springer
Page : 200 pages
File Size : 41,9 Mb
Release : 2006-11-17
Category : Mathematics
ISBN : 9783540392682

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Counterexamples in Topological Vector Spaces by S.M. Khaleelulla Pdf

Author : Alexandre Grothendieck
Publisher : Taylor & Francis Group
Page : 264 pages
File Size : 45,6 Mb
Release : 1973
Category : Linear topological spaces
ISBN : UCAL:B4405273

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Topological Vector Spaces by Alexandre Grothendieck Pdf

Author : Yau-Chuen Wong
Publisher : Routledge
Page : 206 pages
File Size : 47,7 Mb
Release : 2019-01-25
Category : Mathematics
ISBN : 9781351436458

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Introductory Theory of Topological Vector SPates by Yau-Chuen Wong Pdf

This text offers an overview of the basic theories and techniques of functional analysis and its applications. It contains topics such as the fixed point theory starting from Ky Fan's KKM covering and quasi-Schwartz operators. It also includes over 200 exercises to reinforce important concepts.;The author explores three fundamental results on Banach spaces, together with Grothendieck's structure theorem for compact sets in Banach spaces (including new proofs for some standard theorems) and Helley's selection theorem. Vector topologies and vector bornologies are examined in parallel, and their internal and external relationships are studied. This volume also presents recent developments on compact and weakly compact operators and operator ideals; and discusses some applications to the important class of Schwartz spaces.;This text is designed for a two-term course on functional analysis for upper-level undergraduate and graduate students in mathematics, mathematical physics, economics and engineering. It may also be used as a self-study guide by researchers in these disciplines.

Author : John L Kelley
Publisher : Hassell Street Press
Page : 280 pages
File Size : 55,8 Mb
Release : 2021-09-09
Category : Electronic
ISBN : 1014254035

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Linear Topological Spaces by John L Kelley Pdf

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.