Download or read book Locally Convex Spaces written by M. Scott Osborne and published by Springer Science & Business Media. This book was released on 2013-11-08 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: For 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.
Download or read book Locally Convex Spaces written by and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 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.
Download or read book Locally Convex Spaces over Non Archimedean Valued Fields written by C. Perez-Garcia and published by Cambridge University Press. This book was released on 2010-01-07 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-Archimedean functional analysis, where alternative but equally valid number systems such as p-adic numbers are fundamental, is a fast-growing discipline widely used not just within pure mathematics, but also applied in other sciences, including physics, biology and chemistry. This book is the first to provide a comprehensive treatment of non-Archimedean locally convex spaces. The authors provide a clear exposition of the basic theory, together with complete proofs and new results from the latest research. A guide to the many illustrative examples provided, end-of-chapter notes and glossary of terms all make this book easily accessible to beginners at the graduate level, as well as specialists from a variety of disciplines.
Download or read book Barrelled Locally Convex Spaces written by P. Pérez Carreras and published by Elsevier. This book was released on 1987-03-01 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a systematic treatment of barrelled spaces, and of structures in which barrelledness conditions are significant. It is a fairly self-contained study of the structural theory of those spaces, concentrating on the basic phenomena in the theory, and presenting a variety of functional-analytic techniques.Beginning with some basic and important results in different branches of Analysis, the volume deals with Baire spaces, presents a variety of techniques, and gives the necessary definitions, exploring conditions on discs to ensure that they are absorbed by the barrels of the space. The abstract theory of barrelled spaces is then presented, as well as local completeness and its applications to the inheritance of the Mackey topology to subspaces. Further discussed is the abstract study of bornological and ultrabornological spaces; B- and Br-completeness; inductive limits; strong barrelledness conditions; characterizations of barrelled, bornological and (DF)-spaces in the context of spaces of type C(X); the stability of barrelledness conditions of topological tensor products and the related questions of commutability of inductive limits and tensor products; and the holomorphically significant properties of locally convex spaces as developed by Nachbin and others.
Download or read book Locally Convex Spaces and Linear Partial Differential Equations written by François Treves and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is hardly an exaggeration to say that, if the study of general topolog ical vector spaces is justified at all, it is because of the needs of distribu tion and Linear PDE * theories (to which one may add the theory of convolution in spaces of hoi om orphic functions). The theorems based on TVS ** theory are generally of the "foundation" type: they will often be statements of equivalence between, say, the existence - or the approx imability -of solutions to an equation Pu = v, and certain more "formal" properties of the differential operator P, for example that P be elliptic or hyperboJic, together with properties of the manifold X on which P is defined. The latter are generally geometric or topological, e. g. that X be P-convex (Definition 20. 1). Also, naturally, suitable conditions will have to be imposed upon the data, the v's, and upon the stock of possible solutions u. The effect of such theorems is to subdivide the study of an equation like Pu = v into two quite different stages. In the first stage, we shall look for the relevant equivalences, and if none is already available in the literature, we shall try to establish them. The second stage will consist of checking if the "formal" or "geometric" conditions are satisfied.
Download or read book The Best Approximation and Optimization in Locally Convex Spaces written by George Isac and published by Frankfurt am Main : P. Lang. This book was released on 1993 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents several new results on the best simultaneous approximation in locally convex spaces. The concept of nuclear cone is systematically used to establish some interesting relations with Pareto optimization and the duality for vectorial optimization programs with multifunctions.
Download or read book Locally Convex Spaces and Harmonic Analysis An Introduction written by Philippe G. Ciarlet and published by SIAM. This book was released on 2021-08-10 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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.
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.
Download or read book Topological Vector Spaces and Their Applications written by V.I. Bogachev and published by Springer. This book was released on 2017-05-16 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Topics in Locally Convex Spaces written by M. Valdivia and published by Elsevier. This book was released on 1982-08-01 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics in Locally Convex Spaces
Download or read book Topological Vector Spaces I written by Gottfried Köthe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Topological Vector Spaces written by Lawrence Narici and published by CRC Press. This book was released on 2010-07-26 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Topological Vector Spaces and Distributions written by John Horvath and published by Courier Corporation. This book was released on 2013-10-03 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Topological Vector Spaces written by Gottfried Köthe and published by Springer. This book was released on 1983 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Bochner Integral written by J. Mikusinski and published by Birkhäuser. This book was released on 2013-11-11 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of the Lebesgue integral is still considered as a difficult theory, no matter whether it is based the concept of measure or introduced by other methods. The primary aim of this book is to give an approach which would be as intelligible and lucid as possible. Our definition, produced in Chapter I, requires for its background only a little of the theory of absolutely convergent series so that it is understandable for students of the first undergraduate course. Nevertheless, it yields the Lebesgue integral in its full generality and, moreover, extends automatically to the Bochner integral (by replacing real coefficients of series by elements of a Banach space). It seems that our approach is simple enough as to eliminate the less useful Riemann integration theory from regular mathematics courses. Intuitively, the difference between various approaches to integration may be brought out by the following story on shoemakers. A piece of leather, like in Figure 1, is given. The task consists in measuring its area. There are three shoemakers and each of them solves the task in his own way. A B Fig. 1 The shoemaker R. divides the leather into a finite number of vertical strips and considers the strips approximately as rectangles. The sum of areas of all rectangles is taken for an approximate area of the leather (Figure 2). If he is not satisfied with the obtained exactitude, he repeats the whole procedure, by dividing the leather into thinner strips.
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"--
Download or read book Real and Functional Analysis written by Vladimir I. Bogachev and published by Springer Nature. This book was released on 2020-02-25 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on lectures given at "Mekhmat", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis. Featuring an advanced course on real and functional analysis, the book presents not only core material traditionally included in university courses of different levels, but also a survey of the most important results of a more subtle nature, which cannot be considered basic but which are useful for applications. Further, it includes several hundred exercises of varying difficulty with tips and references. The book is intended for graduate and PhD students studying real and functional analysis as well as mathematicians and physicists whose research is related to functional analysis.
