Topics in Locally Convex Spaces
Author: M. Valdivia
Publisher: Elsevier
Published: 1982-08-01
Total Pages: 525
ISBN-13: 008087178X
DOWNLOAD EBOOKTopics in Locally Convex Spaces
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Locally Convex Spaces
Author: M. Scott Osborne
Publisher: Springer Science & Business Media
Published: 2013-11-08
Total Pages: 217
ISBN-13: 3319020455
DOWNLOAD EBOOKFor most practicing analysts who use functional analysis, the restriction to Banach spaces seen in most real analysis graduate texts is not enough for their research. This graduate text, while focusing on locally convex topological vector spaces, is intended to cover most of the general theory needed for application to other areas of analysis. Normed vector spaces, Banach spaces, and Hilbert spaces are all examples of classes of locally convex spaces, which is why this is an important topic in functional analysis. While this graduate text focuses on what is needed for applications, it also shows the beauty of the subject and motivates the reader with exercises of varying difficulty. Key topics covered include point set topology, topological vector spaces, the Hahn–Banach theorem, seminorms and Fréchet spaces, uniform boundedness, and dual spaces. The prerequisite for this text is the Banach space theory typically taught in a beginning graduate real analysis course.
Locally Convex Spaces
Author:
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 549
ISBN-13: 3322905594
DOWNLOAD EBOOKThe present book grew out of several courses which I have taught at the University of Zürich and at the University of Maryland during the past seven years. It is primarily intended to be a systematic text on locally convex spaces at the level of a student who has some familiarity with general topology and basic measure theory. However, since much of the material is of fairly recent origin and partly appears here for the first time in a book, and also since some well-known material has been given a not so well-known treatment, I hope that this book might prove useful even to more advanced readers. And in addition I hope that the selection ofmaterial marks a sufficient set-offfrom the treatments in e.g. N. Bourbaki [4], [5], R.E. Edwards [1], K. Floret-J. Wloka [1], H.G. Garnir-M. De Wilde-J. Schmets [1], AGrothendieck [13], H. Heuser [1], J. Horvath [1], J.L. Kelley-I. Namioka et al. [1], G. Köthe [7], [10], A P. Robertson W. Robertson [1], W. Rudin [2], H.H. Schaefer [1], F. Treves [l], A Wilansky [1]. A few sentences should be said about the organization of the book. It consists of 21 chapters which are grouped into three parts. Each chapter splits into several sections. Chapters, sections, and the statements therein are enumerated in consecutive fashion.
Locally Convex Spaces and Harmonic Analysis: An Introduction
Author: Philippe G. Ciarlet
Publisher: SIAM
Published: 2021-08-10
Total Pages: 203
ISBN-13: 1611976650
DOWNLOAD EBOOKThis self-contained textbook covers the fundamentals of two basic topics of linear functional analysis: locally convex spaces and harmonic analysis. Readers will find detailed introductions to topological vector spaces, distribution theory, weak topologies, the Fourier transform, the Hilbert transform, and Calderón–Zygmund singular integrals. An ideal introduction to more advanced texts, the book complements Ciarlet’s Linear and Nonlinear Functional Analysis with Applications (SIAM), in which these two topics were not treated. Pedagogical features such as detailed proofs and 93 problems make the book ideal for a one-semester first-year graduate course or for self-study. The book is intended for advanced undergraduates and first-year graduate students and researchers. It is appropriate for courses on functional analysis, distribution theory, Fourier transform, and harmonic analysis.
A Course on Topological Vector Spaces
Author: Jürgen Voigt
Publisher: Springer Nature
Published: 2020-03-06
Total Pages: 152
ISBN-13: 3030329453
DOWNLOAD EBOOKThis 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.
Applied Numerical Linear Algebra
Author: James W. Demmel
Publisher: SIAM
Published: 1997-08-01
Total Pages: 426
ISBN-13: 0898713897
DOWNLOAD EBOOKThis comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.
Topological Vector Spaces, Distributions and Kernels
Author: François Treves
Publisher: Elsevier
Published: 2016-06-03
Total Pages: 582
ISBN-13: 1483223620
DOWNLOAD EBOOKTopological 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.
Complex Analysis in Locally Convex Spaces
Author: S. Dineen
Publisher: Elsevier
Published: 2011-08-18
Total Pages: 507
ISBN-13: 0080871682
DOWNLOAD EBOOKComplex Analysis in Locally Convex Spaces
Topological Vector Spaces and Distributions
Author: John Horvath
Publisher: Courier Corporation
Published: 2013-10-03
Total Pages: 466
ISBN-13: 0486311031
DOWNLOAD EBOOKPrecise 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.
Advanced Real Analysis
Author: Anthony W. Knapp
Publisher: Springer Science & Business Media
Published: 2008-07-11
Total Pages: 484
ISBN-13: 0817644423
DOWNLOAD EBOOK* Presents a comprehensive treatment with a global view of the subject * Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician
