Topological Vector Spaces And Distributions
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Topological Vector Spaces Distributions And Kernels
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Author : François Treves
language : en
Publisher: Elsevier
Release Date : 2016-06-03
Topological Vector Spaces Distributions And Kernels written by François Treves and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-03 with Mathematics categories.
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.
Topological Vector Spaces Distributions And Kernels
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Author :
language : en
Publisher: Academic Press
Release Date : 1967-01-01
Topological Vector Spaces Distributions And Kernels written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967-01-01 with Mathematics categories.
Topological Vector Spaces, Distributions and Kernels
Topological Vector Spaces And Distributions
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Author : John Horvath
language : en
Publisher: Courier Corporation
Release Date : 2013-10-03
Topological Vector Spaces And Distributions written by John Horvath and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-03 with Mathematics categories.
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.
Modern Methods In Topological Vector Spaces
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Author : Albert Wilansky
language : en
Publisher: Courier Corporation
Release Date : 2013-11-26
Modern Methods In Topological Vector Spaces written by Albert Wilansky and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-26 with Mathematics categories.
Geared toward beginning graduate students of mathematics, this text covers Banach space, open mapping and closed graph theorems, local convexity, duality, equicontinuity, operators, inductive limits, and compactness and barrelled spaces. 1978 edition.
A Course On Topological Vector Spaces
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Author : Jürgen Voigt
language : en
Publisher: Springer Nature
Release Date : 2020-03-06
A Course On Topological Vector Spaces written by Jürgen Voigt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-06 with Mathematics categories.
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.
Topological Vector Spaces Distributions And Kernels
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Author :
language : en
Publisher:
Release Date : 2006
Topological Vector Spaces Distributions And Kernels written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
Topological Vector Spaces Distributions And Kernels
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Author : François Trèves
language : en
Publisher:
Release Date : 1973
Topological Vector Spaces Distributions And Kernels written by François Trèves and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with categories.
Topological Vector Spaces
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Author : Helmut H. Schaefer
language : en
Publisher:
Release Date : 1971
Topological Vector Spaces written by Helmut H. Schaefer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Linear topological spaces categories.
Intended as a systematic text on topological vector spaces, this text assumes familiarity with the elements of general topology and linear algebra. Similarly, the elementary facts on Hilbert and Banach spaces are not discussed in detail here, since the book is mainly addressed to those readers who wish to go beyond the introductory level. Each of the chapters is preceded by an introduction and followed by exercises, which in turn are devoted to further results and supplements, in particular, to examples and counter-examples, and hints have been given where appropriate.
Topological Vector Spaces Distributions And Kernels
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Author : Francois Treves
language : en
Publisher:
Release Date : 1967
Topological Vector Spaces Distributions And Kernels written by Francois Treves and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Analyse fonctionnelle categories.
The Prehistory Of The Theory Of Distributions
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Author : J. Lützen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Prehistory Of The Theory Of Distributions written by J. Lützen 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.
I first learned the theory of distributions from Professor Ebbe Thue Poulsen in an undergraduate course at Aarhus University. Both his lectures and the textbook, Topological Vector Spaces, Distributions and Kernels by F. Treves, used in the course, opened my eyes to the beauty and abstract simplicity of the theory. However my incomplete study of many branches of classical analysis left me with the question: Why is the theory of distributions important? In my continued studies this question was gradually answered, but my growing interest in the history of mathematics caused me to alter my question to other questions such as: For what purpose, if any, was the theory of distributions originally created? Who invented distributions and when? I quickly found answers to the last two questions: distributions were invented by S. Sobolev and L. Schwartz around 1936 and 1950, respectively. Knowing this answer, however, only created a new question: Did Sobolev and Schwartz construct distributions from scratch or were there earlier trends and, if so, what were they? It is this question, concerning the pre history of the theory of distributions, which I attempt to answer in this book. Most of my research took place at the History of Science Department of Aarhus University. I wish to thank this department for its financial and intellectual support. I am especially grateful to Lektors Kirsti Andersen from the History of Science Department and Lars Mejlbo from the Mathematics Department, for their kindness, constructive criticism, and encouragement.