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Author : Mahlon M. Day
Publisher : Springer Science & Business Media
ISBN 13 : 3662090007
Total Pages : 222 pages
Book Rating : 4.6/5 (62 download)
Download or read book Normed Linear Spaces written by Mahlon M. Day and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Rodney Coleman
Publisher : Springer Science & Business Media
ISBN 13 : 1461438942
Total Pages : 255 pages
Book Rating : 4.4/5 (614 download)
Download or read book Calculus on Normed Vector Spaces written by Rodney Coleman and published by Springer Science & Business Media. This book was released on 2012-07-25 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as an introduction to calculus on normed vector spaces at a higher undergraduate or beginning graduate level. The prerequisites include basic calculus and linear algebra, as well as a certain mathematical maturity. All the important topology and functional analysis topics are introduced where necessary. In its attempt to show how calculus on normed vector spaces extends the basic calculus of functions of several variables, this book is one of the few textbooks to bridge the gap between the available elementary texts and high level texts. The inclusion of many non-trivial applications of the theory and interesting exercises provides motivation for the reader.
Author : J. R. Giles
Publisher : Cambridge University Press
ISBN 13 : 9780521653756
Total Pages : 298 pages
Book Rating : 4.6/5 (537 download)
Download or read book Introduction to the Analysis of Normed Linear Spaces written by J. R. Giles and published by Cambridge University Press. This book was released on 2000-03-13 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a basic course in functional analysis for senior undergraduate and beginning postgraduate students. The reader need only be familiarity with elementary real and complex analysis, linear algebra and have studied a course in the analysis of metric spaces; knowledge of integration theory or general topology is not required. The text concerns the structural properties of normed linear spaces in general, especially associated with dual spaces and continuous linear operators on normed linear spaces. The implications of the general theory are illustrated with a great variety of example spaces.
Author :
Publisher : Elsevier
ISBN 13 : 0080871798
Total Pages : 321 pages
Book Rating : 4.0/5 (88 download)
Download or read book Introduction to Banach Spaces and their Geometry written by and published by Elsevier. This book was released on 2011-10-10 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Banach Spaces and their Geometry
Author : Ole Christensen
Publisher : Springer Science & Business Media
ISBN 13 : 0817649808
Total Pages : 280 pages
Book Rating : 4.8/5 (176 download)
Download or read book Functions, Spaces, and Expansions written by Ole Christensen and published by Springer Science & Business Media. This book was released on 2010-05-27 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level textbook is a detailed exposition of key mathematical tools in analysis aimed at students, researchers, and practitioners across science and engineering. Every topic covered has been specifically chosen because it plays a key role outside the field of pure mathematics. Although the treatment of each topic is mathematical in nature, and concrete applications are not delineated, the principles and tools presented are fundamental to exploring the computational aspects of physics and engineering. Readers are expected to have a solid understanding of linear algebra, in Rn and in general vector spaces. Familiarity with the basic concepts of calculus and real analysis, including Riemann integrals and infinite series of real or complex numbers, is also required.
Author : E. Suhubi
Publisher : Springer Science & Business Media
ISBN 13 : 9401701415
Total Pages : 702 pages
Book Rating : 4.4/5 (17 download)
Download or read book Functional Analysis written by E. Suhubi and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional Analysis is primarily concerned with the structure of infinite dimensional vector spaces and the transformations, which are frequently called operators, between such spaces. The elements of these vector spaces are usually functions with certain properties, which map one set into another. Functional analysis became one of the success stories of mathematics in the 20th century, in the search for generality and unification.
Author : Tsoy-Wo Ma
Publisher : World Scientific
ISBN 13 : 9789810221379
Total Pages : 378 pages
Book Rating : 4.2/5 (213 download)
Download or read book Classical Analysis on Normed Spaces written by Tsoy-Wo Ma and published by World Scientific. This book was released on 1995 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an elementary introduction to the classical analysis on normed spaces, paying special attention to nonlinear topics such as fixed points, calculus and ordinary differential equations. It is aimed at beginners who want to get through the basic material as soon as possible and then move on to do their own research immediately. It assumes only general knowledge in finite-dimensional linear algebra, simple calculus and elementary complex analysis. Since the treatment is self-contained with sufficient details, even an undergraduate with mathematical maturity should have no problem working through it alone. Various chapters can be integrated into parts of a Master degree program by course work organized by any regional university. Restricted to finite-dimensional spaces rather than normed spaces, selected chapters can be used for a course in advanced calculus. Engineers and physicists may find this book a handy reference in classical analysis.
Author : Carlo Alabiso
Publisher : Springer
ISBN 13 : 3319037137
Total Pages : 267 pages
Book Rating : 4.3/5 (19 download)
Download or read book A Primer on Hilbert Space Theory written by Carlo Alabiso and published by Springer. This book was released on 2014-10-08 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, resides in the very high mathematical difficulty of even the simplest physical case. Within an ordinary graduate course in physics there is insufficient time to cover the theory of Hilbert spaces and operators, as well as distribution theory, with sufficient mathematical rigor. Compromises must be found between full rigor and practical use of the instruments. The book is based on the author's lessons on functional analysis for graduate students in physics. It will equip the reader to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. With respect to the original lectures, the mathematical flavor in all subjects has been enriched. Moreover, a brief introduction to topological groups has been added in addition to exercises and solved problems throughout the text. With these improvements, the book can be used in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.
Author : Bryan Rynne
Publisher : Springer Science & Business Media
ISBN 13 : 1447136551
Total Pages : 276 pages
Book Rating : 4.4/5 (471 download)
Download or read book Linear Functional Analysis written by Bryan Rynne and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the ideas and methods of linear func tional analysis at a level appropriate to the final year of an undergraduate course at a British university. The prerequisites for reading it are a standard undergraduate knowledge of linear algebra and real analysis (including the the ory of metric spaces). Part of the development of functional analysis can be traced to attempts to find a suitable framework in which to discuss differential and integral equa tions. Often, the appropriate setting turned out to be a vector space of real or complex-valued functions defined on some set. In general, such a vector space is infinite-dimensional. This leads to difficulties in that, although many of the elementary properties of finite-dimensional vector spaces hold in infinite dimensional vector spaces, many others do not. For example, in general infinite dimensional vector spaces there is no framework in which to make sense of an alytic concepts such as convergence and continuity. Nevertheless, on the spaces of most interest to us there is often a norm (which extends the idea of the length of a vector to a somewhat more abstract setting). Since a norm on a vector space gives rise to a metric on the space, it is now possible to do analysis in the space. As real or complex-valued functions are often called functionals, the term functional analysis came to be used for this topic. We now briefly outline the contents of the book.
Author : Gottfried Köthe
Publisher : Springer Science & Business Media
ISBN 13 : 3642649882
Total Pages : 470 pages
Book Rating : 4.6/5 (426 download)
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.
Author : Karen Saxe
Publisher : Springer Science & Business Media
ISBN 13 : 1475736878
Total Pages : 209 pages
Book Rating : 4.4/5 (757 download)
Download or read book Beginning Functional Analysis written by Karen Saxe and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: The unifying approach of functional analysis is to view functions as points in abstract vector space and the differential and integral operators as linear transformations on these spaces. The author's goal is to present the basics of functional analysis in a way that makes them comprehensible to a student who has completed courses in linear algebra and real analysis, and to develop the topics in their historical contexts.
Author : Jacob Korevaar
Publisher :
ISBN 13 :
Total Pages : 528 pages
Book Rating : 4.3/5 (91 download)
Download or read book Mathematical Methods: Linear algebra, normed spaces, distributions, integration written by Jacob Korevaar and published by . This book was released on 1968 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Stefan Cobzas
Publisher : Springer Science & Business Media
ISBN 13 : 3034804784
Total Pages : 229 pages
Book Rating : 4.0/5 (348 download)
Download or read book Functional Analysis in Asymmetric Normed Spaces written by Stefan Cobzas and published by Springer Science & Business Media. This book was released on 2012-10-30 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: An asymmetric norm is a positive definite sublinear functional p on a real vector space X. The topology generated by the asymmetric norm p is translation invariant so that the addition is continuous, but the asymmetry of the norm implies that the multiplication by scalars is continuous only when restricted to non-negative entries in the first argument. The asymmetric dual of X, meaning the set of all real-valued upper semi-continuous linear functionals on X, is merely a convex cone in the vector space of all linear functionals on X. In spite of these differences, many results from classical functional analysis have their counterparts in the asymmetric case, by taking care of the interplay between the asymmetric norm p and its conjugate. Among the positive results one can mention: Hahn–Banach type theorems and separation results for convex sets, Krein–Milman type theorems, analogs of the fundamental principles – open mapping, closed graph and uniform boundedness theorems – an analog of the Schauder’s theorem on the compactness of the conjugate mapping. Applications are given to best approximation problems and, as relevant examples, one considers normed lattices equipped with asymmetric norms and spaces of semi-Lipschitz functions on quasi-metric spaces. Since the basic topological tools come from quasi-metric spaces and quasi-uniform spaces, the first chapter of the book contains a detailed presentation of some basic results from the theory of these spaces. The focus is on results which are most used in functional analysis – completeness, compactness and Baire category – which drastically differ from those in metric or uniform spaces. The book is fairly self-contained, the prerequisites being the acquaintance with the basic results in topology and functional analysis, so it may be used for an introduction to the subject. Since new results, in the focus of current research, are also included, researchers in the area can use it as a reference text.
Author : Yutaka Yamamoto
Publisher : SIAM
ISBN 13 : 1611972302
Total Pages : 270 pages
Book Rating : 4.6/5 (119 download)
Download or read book From Vector Spaces to Function Spaces written by Yutaka Yamamoto and published by SIAM. This book was released on 2012-10-31 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to analytic methods in applied mathematics from the perspective of functional analysis, suitable for scientists, engineers and students.
Author : Raymond W. Freese
Publisher : Nova Publishers
ISBN 13 : 9781590330197
Total Pages : 314 pages
Book Rating : 4.3/5 (31 download)
Download or read book Geometry of Linear 2-normed Spaces written by Raymond W. Freese and published by Nova Publishers. This book was released on 2001 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert E. Megginson
Publisher : Springer Science & Business Media
ISBN 13 : 1461206030
Total Pages : 613 pages
Book Rating : 4.4/5 (612 download)
Download or read book An Introduction to Banach Space Theory written by Robert E. Megginson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preparing students for further study of both the classical works and current research, this is an accessible text for students who have had a course in real and complex analysis and understand the basic properties of L p spaces. It is sprinkled liberally with examples, historical notes, citations, and original sources, and over 450 exercises provide practice in the use of the results developed in the text through supplementary examples and counterexamples.
Author : Rabindranath Sen
Publisher : Anthem Press
ISBN 13 : 1783083247
Total Pages : 486 pages
Book Rating : 4.7/5 (83 download)
Download or read book A First Course in Functional Analysis written by Rabindranath Sen and published by Anthem Press. This book was released on 2014-11-01 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the reader with a comprehensive introduction to functional analysis. Topics include normed linear and Hilbert spaces, the Hahn-Banach theorem, the closed graph theorem, the open mapping theorem, linear operator theory, the spectral theory, and a brief introduction to the Lebesgue measure. The book explains the motivation for the development of these theories, and applications that illustrate the theories in action. Applications in optimal control theory, variational problems, wavelet analysis and dynamical systems are also highlighted. ‘A First Course in Functional Analysis’ will serve as a ready reference to students not only of mathematics, but also of allied subjects in applied mathematics, physics, statistics and engineering.
