Advances In The Theory Of Frechet Spaces

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Advances in the Theory of Fréchet Spaces

Author : T. Terziogammalu
Publisher : Springer Science & Business Media
ISBN 13 : 9400924569
Total Pages : 375 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Advances in the Theory of Fréchet Spaces by : T. Terziogammalu

Download or read book Advances in the Theory of Fréchet Spaces written by T. Terziogammalu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: Frechet spaces have been studied since the days of Banach. These spaces, their inductive limits and their duals played a prominent role in the development of the theory of locally convex spaces. Also they are natural tools in many areas of real and complex analysis. The pioneering work of Grothendieck in the fifties has been one of the important sources of inspiration for research in the theory of Frechet spaces. A structure theory of nuclear Frechet spaces emerged and some important questions posed by Grothendieck were settled in the seventies. In particular, subspaces and quotient spaces of stable nuclear power series spaces were completely characterized. In the last years it has become increasingly clear that the methods used in the structure theory of nuclear Frechet spaces actually provide new insight to linear problems in diverse branches of analysis and lead to solutions of some classical problems. The unifying theme at our Workshop was the recent developments in the theory of the projective limit functor. This is appropriate because of the important role this theory had in the recent research. The main results of the structure theory of nuclear Frechet spaces can be formulated and proved within the framework of this theory. A major area of application of the theory of the projective limit functor is to decide when a linear operator is surjective and, if it is, to determine whether it has a continuous right inverse.

Advances in the Theory of Frechet Spaces

Author : T Terziogammalu
Publisher :
ISBN 13 : 9789400924574
Total Pages : 384 pages
Book Rating : 4.9/5 (245 download)

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Book Synopsis Advances in the Theory of Frechet Spaces by : T Terziogammalu

Download or read book Advances in the Theory of Frechet Spaces written by T Terziogammalu and published by . This book was released on 1989-09-30 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advances in the Theory of Frechet Spaces

Author : T. Terzioglu
Publisher :
ISBN 13 :
Total Pages : 363 pages
Book Rating : 4.:/5 (928 download)

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Book Synopsis Advances in the Theory of Frechet Spaces by : T. Terzioglu

Download or read book Advances in the Theory of Frechet Spaces written by T. Terzioglu and published by . This book was released on 1989 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fundamentals of Advanced Mathematics V2

Author : Henri Bourles
Publisher : Elsevier
ISBN 13 : 0081023855
Total Pages : 362 pages
Book Rating : 4.0/5 (81 download)

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Book Synopsis Fundamentals of Advanced Mathematics V2 by : Henri Bourles

Download or read book Fundamentals of Advanced Mathematics V2 written by Henri Bourles and published by Elsevier. This book was released on 2018-02-03 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three volumes of this series of books, of which this is the second, put forward the mathematical elements that make up the foundations of a number of contemporary scientific methods: modern theory on systems, physics and engineering. Whereas the first volume focused on the formal conditions for systems of linear equations (in particular of linear differential equations) to have solutions, this book presents the approaches to finding solutions to polynomial equations and to systems of linear differential equations with varying coefficients. Fundamentals of Advanced Mathematics, Volume 2: Field Extensions, Topology and Topological Vector Spaces, Functional Spaces, and Sheaves begins with the classical Galois theory and the theory of transcendental field extensions. Next, the differential side of these theories is treated, including the differential Galois theory (Picard-Vessiot theory of systems of linear differential equations with time-varying coefficients) and differentially transcendental field extensions. The treatment of analysis includes topology (using both filters and nets), topological vector spaces (using the notion of disked space, which simplifies the theory of duality), and the radon measure (assuming that the usual theory of measure and integration is known). In addition, the theory of sheaves is developed with application to the theory of distributions and the theory of hyperfunctions (assuming that the usual theory of functions of the complex variable is known). This volume is the prerequisite to the study of linear systems with time-varying coefficients from the point-of-view of algebraic analysis and the algebraic theory of nonlinear systems. - Present Galois Theory, transcendental field extensions, and Picard - Includes sections on Vessiot theory, differentially transcendental field extensions, topology, topological vector spaces, Radon measure, differential calculus in Banach spaces, sheaves, distributions, hyperfunctions, algebraic analysis, and local analysis of systems of linear differential equations

Progress in Functional Analysis

Author : K.D. Bierstedt
Publisher : Elsevier
ISBN 13 : 0080872816
Total Pages : 461 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Progress in Functional Analysis by : K.D. Bierstedt

Download or read book Progress in Functional Analysis written by K.D. Bierstedt and published by Elsevier. This book was released on 1992-01-10 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume includes a collection of research articles inFunctional Analysis, celebrating the occasion of Manuel Valdivia'ssixtieth birthday. The papers included in the volume are basedon the main lectures presented during the internationalfunctional analysis meeting held in Peñíscola(Valencia, Spain) in October 1990.During his career, Valdiviahas made contributions to a wide variety of areas of FunctionalAnalysis and his work has had a profound impact. A thoroughappreciation of Valdivia's work is presented in J.Horváth's article. In honor of Valdivia's achievements, this volume presents more than twenty-five papers on topics related to his research(Banach spaces, operator ideals, tensor products, Fréchet,(DF) and (LF) spaces, distribution theory, infinite holomorphyetc.). While the majority of papers are research articles, survey articles are also included. The book covers a broad spectrum of interests in today's Functional Analysis and presents new results by leading specialists in the field.

Topological Vector Spaces, Distributions and Kernels

Author : François Treves
Publisher : Elsevier
ISBN 13 : 1483223620
Total Pages : 582 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Topological Vector Spaces, Distributions and Kernels by : François Treves

Download or read book Topological Vector Spaces, Distributions and Kernels written by François Treves and published by Elsevier. This book was released on 2016-06-03 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Recent Progress in Functional Analysis

Author : K.D. Bierstedt
Publisher : Elsevier
ISBN 13 : 0080515924
Total Pages : 469 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Recent Progress in Functional Analysis by : K.D. Bierstedt

Download or read book Recent Progress in Functional Analysis written by K.D. Bierstedt and published by Elsevier. This book was released on 2001-09-20 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Proceedings Volume contains 32 articles on various interesting areas ofpresent-day functional analysis and its applications: Banach spaces andtheir geometry, operator ideals, Banach and operator algebras, operator andspectral theory, Frechet spaces and algebras, function and sequence spaces.The authors have taken much care with their articles and many papers presentimportant results and methods in active fields of research. Several surveytype articles (at the beginning and the end of the book) will be very usefulfor mathematicians who want to learn "what is going on" in some particularfield of research.

A Course on Topological Vector Spaces

Author : Jürgen Voigt
Publisher : Springer Nature
ISBN 13 : 3030329453
Total Pages : 152 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis A Course on Topological Vector Spaces by : Jürgen Voigt

Download or read book A Course on Topological Vector Spaces written by Jürgen Voigt and published by Springer Nature. This book was released on 2020-03-06 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Descriptive Topology in Selected Topics of Functional Analysis

Author : Jerzy Kąkol
Publisher : Springer Science & Business Media
ISBN 13 : 1461405297
Total Pages : 494 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Descriptive Topology in Selected Topics of Functional Analysis by : Jerzy Kąkol

Download or read book Descriptive Topology in Selected Topics of Functional Analysis written by Jerzy Kąkol and published by Springer Science & Business Media. This book was released on 2011-08-30 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Descriptive Topology in Selected Topics of Functional Analysis" is a collection of recent developments in the field of descriptive topology, specifically focused on the classes of infinite-dimensional topological vector spaces that appear in functional analysis. Such spaces include Fréchet spaces, (LF)-spaces and their duals, and the space of continuous real-valued functions C(X) on a completely regular Hausdorff space X, to name a few. These vector spaces appear in functional analysis in distribution theory, differential equations, complex analysis, and various other analytical settings. This monograph provides new insights into the connections between the topological properties of linear function spaces and their applications in functional analysis.

Topology and Approximate Fixed Points

Author : Afif Ben Amar
Publisher : Springer Nature
ISBN 13 : 3030922049
Total Pages : 258 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Topology and Approximate Fixed Points by : Afif Ben Amar

Download or read book Topology and Approximate Fixed Points written by Afif Ben Amar and published by Springer Nature. This book was released on 2022-01-25 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines in detail approximate fixed point theory in different classes of topological spaces for general classes of maps. It offers a comprehensive treatment of the subject that is up-to-date, self-contained, and rich in methods, for a wide variety of topologies and maps. Content includes known and recent results in topology (with proofs), as well as recent results in approximate fixed point theory. This work starts with a set of basic notions in topological spaces. Special attention is given to topological vector spaces, locally convex spaces, Banach spaces, and ultrametric spaces. Sequences and function spaces—and fundamental properties of their topologies—are also covered. The reader will find discussions on fundamental principles, namely the Hahn-Banach theorem on extensions of linear (bounded) functionals; the Banach open mapping theorem; the Banach-Steinhaus uniform boundedness principle; and Baire categories, including some applications. Also included are weak topologies and their properties, in particular the theorems of Eberlein-Smulian, Goldstine, Kakutani, James and Grothendieck, reflexive Banach spaces, l_{1}- sequences, Rosenthal's theorem, sequential properties of the weak topology in a Banach space and weak* topology of its dual, and the Fréchet-Urysohn property. The subsequent chapters cover various almost fixed point results, discussing how to reach or approximate the unique fixed point of a strictly contractive mapping of a spherically complete ultrametric space. They also introduce synthetic approaches to fixed point problems involving regular-global-inf functions. The book finishes with a study of problems involving approximate fixed point property on an ambient space with different topologies. By providing appropriate background and up-to-date research results, this book can greatly benefit graduate students and mathematicians seeking to advance in topology and fixed point theory.

Modern Methods in Topological Vector Spaces

Author : Albert Wilansky
Publisher : Courier Corporation
ISBN 13 : 0486493539
Total Pages : 324 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Modern Methods in Topological Vector Spaces by : Albert Wilansky

Download or read book Modern Methods in Topological Vector Spaces written by Albert Wilansky and published by Courier Corporation. This book was released on 2013-01-01 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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"--

Recent Progress in General Topology II

Author : M. Husek
Publisher : Elsevier
ISBN 13 : 0080929958
Total Pages : 651 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Recent Progress in General Topology II by : M. Husek

Download or read book Recent Progress in General Topology II written by M. Husek and published by Elsevier. This book was released on 2002-11-13 with total page 651 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents surveys describing recent developments in most of the primary subfields ofGeneral Topology and its applications to Algebra and Analysis during the last decade. It follows freelythe previous edition (North Holland, 1992), Open Problems in Topology (North Holland, 1990) and Handbook of Set-Theoretic Topology (North Holland, 1984). The book was prepared inconnection with the Prague Topological Symposium, held in 2001. During the last 10 years the focusin General Topology changed and therefore the selection of topics differs slightly from thosechosen in 1992. The following areas experienced significant developments: Topological Groups, Function Spaces, Dimension Theory, Hyperspaces, Selections, Geometric Topology (includingInfinite-Dimensional Topology and the Geometry of Banach Spaces). Of course, not every important topic could be included in this book. Except surveys, the book contains several historical essays written by such eminent topologists as:R.D. Anderson, W.W. Comfort, M. Henriksen, S. Mardeŝić, J. Nagata, M.E. Rudin, J.M. Smirnov (several reminiscences of L. Vietoris are added). In addition to extensive author and subject indexes, a list of all problems and questions posed in this book are added. List of all authors of surveys: A. Arhangel'skii, J. Baker and K. Kunen, H. Bennett and D. Lutzer, J. Dijkstra and J. van Mill, A. Dow, E. Glasner, G. Godefroy, G. Gruenhage, N. Hindman and D. Strauss, L. Hola and J. Pelant, K. Kawamura, H.-P. Kuenzi, W. Marciszewski, K. Martin and M. Mislove and M. Reed, R. Pol and H. Torunczyk, D. Repovs and P. Semenov, D. Shakhmatov, S. Solecki, M. Tkachenko.

Derived Functors in Functional Analysis

Author : Jochen Wengenroth
Publisher : Springer
ISBN 13 : 3540362118
Total Pages : 141 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Derived Functors in Functional Analysis by : Jochen Wengenroth

Download or read book Derived Functors in Functional Analysis written by Jochen Wengenroth and published by Springer. This book was released on 2003-01-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text contains for the first time in book form the state of the art of homological methods in functional analysis like characterizations of the vanishing of the derived projective limit functor or the functors Ext1 (E, F) for Fréchet and more general spaces. The researcher in real and complex analysis finds powerful tools to solve surjectivity problems e.g. on spaces of distributions or to characterize the existence of solution operators. The requirements from homological algebra are minimized: all one needs is summarized on a few pages. The answers to several questions of V.P. Palamodov who invented homological methods in analysis also show the limits of the program.

Advanced Functional Analysis

Author : Eberhard Malkowsky
Publisher : CRC Press
ISBN 13 : 0429809557
Total Pages : 446 pages
Book Rating : 4.4/5 (298 download)

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Book Synopsis Advanced Functional Analysis by : Eberhard Malkowsky

Download or read book Advanced Functional Analysis written by Eberhard Malkowsky and published by CRC Press. This book was released on 2019-02-25 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional analysis and operator theory are widely used in the description, understanding and control of dynamical systems and natural processes in physics, chemistry, medicine and the engineering sciences. Advanced Functional Analysis is a self-contained and comprehensive reference for advanced functional analysis and can serve as a guide for related research. The book can be used as a textbook in advanced functional analysis, which is a modern and important field in mathematics, for graduate and postgraduate courses and seminars at universities. At the same time, it enables the interested readers to do their own research. Features Written in a concise and fluent style Covers a broad range of topics Includes related topics from research

History of Banach Spaces and Linear Operators

Author : Albrecht Pietsch
Publisher : Springer Science & Business Media
ISBN 13 : 0817645969
Total Pages : 877 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis History of Banach Spaces and Linear Operators by : Albrecht Pietsch

Download or read book History of Banach Spaces and Linear Operators written by Albrecht Pietsch and published by Springer Science & Business Media. This book was released on 2007-12-31 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Spectral Decompositions and Analytic Sheaves

Author : Jörg Eschmeier
Publisher : Oxford University Press
ISBN 13 : 9780198536673
Total Pages : 378 pages
Book Rating : 4.5/5 (366 download)

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Book Synopsis Spectral Decompositions and Analytic Sheaves by : Jörg Eschmeier

Download or read book Spectral Decompositions and Analytic Sheaves written by Jörg Eschmeier and published by Oxford University Press. This book was released on 1996 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rapid developments in multivariable spectral theory have led to important and fascinating results which also have applications in other mathematical disciplines. In this book, various concepts from function theory and complex analytic geometry are drawn together to give a new approach to concrete spectral computations and give insights into new developments in the spectral theory of linear operators. Classical results from cohomology theory of Banach algebras, multidimensional spectral theory, and complex analytic geometry have been freshly interpreted using the language of homological algebra. The advantages of this approach are illustrated by a variety of examples, unexpected applications, and conceptually new ideas that should stimulate further research among mathematicians.

Course In Analysis, A - Vol V: Functional Analysis, Some Operator Theory, Theory Of Distributions

Author : Niels Jacob
Publisher : World Scientific
ISBN 13 : 9811215510
Total Pages : 854 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Course In Analysis, A - Vol V: Functional Analysis, Some Operator Theory, Theory Of Distributions by : Niels Jacob

Download or read book Course In Analysis, A - Vol V: Functional Analysis, Some Operator Theory, Theory Of Distributions written by Niels Jacob and published by World Scientific. This book was released on 2020-01-22 with total page 854 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is an advanced textbook and a reference text in functional analysis in the wide sense. It provides advanced undergraduate and graduate students with a coherent introduction to the field, i.e. the basic principles, and leads them to more demanding topics such as the spectral theorem, Choquet theory, interpolation theory, analysis of operator semigroups, Hilbert-Schmidt operators and Hille-Tamarkin operators, topological vector spaces and distribution theory, fundamental solutions, or the Schwartz kernel theorem.All topics are treated in great detail and the text provided is suitable for self-studying the subject. This is enhanced by more than 270 problems solved in detail. At the same time the book is a reference text for any working mathematician needing results from functional analysis, operator theory or the theory of distributions.Embedded as Volume V in the Course of Analysis, readers will have a self-contained treatment of a key area in modern mathematics. A detailed list of references invites to further studies.