Download or read book Introduction to Real Analysis written by Christopher Heil and published by Springer. This book was released on 2019-07-20 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed over years of classroom use, this textbook provides a clear and accessible approach to real analysis. This modern interpretation is based on the author’s lecture notes and has been meticulously tailored to motivate students and inspire readers to explore the material, and to continue exploring even after they have finished the book. The definitions, theorems, and proofs contained within are presented with mathematical rigor, but conveyed in an accessible manner and with language and motivation meant for students who have not taken a previous course on this subject. The text covers all of the topics essential for an introductory course, including Lebesgue measure, measurable functions, Lebesgue integrals, differentiation, absolute continuity, Banach and Hilbert spaces, and more. Throughout each chapter, challenging exercises are presented, and the end of each section includes additional problems. Such an inclusive approach creates an abundance of opportunities for readers to develop their understanding, and aids instructors as they plan their coursework. Additional resources are available online, including expanded chapters, enrichment exercises, a detailed course outline, and much more. Introduction to Real Analysis is intended for first-year graduate students taking a first course in real analysis, as well as for instructors seeking detailed lecture material with structure and accessibility in mind. Additionally, its content is appropriate for Ph.D. students in any scientific or engineering discipline who have taken a standard upper-level undergraduate real analysis course.
Download or read book Optimization on Metric and Normed Spaces written by Alexander J. Zaslavski and published by Springer Science & Business Media. This book was released on 2010-08-05 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Optimization on Metric and Normed Spaces" is devoted to the recent progress in optimization on Banach spaces and complete metric spaces. Optimization problems are usually considered on metric spaces satisfying certain compactness assumptions which guarantee the existence of solutions and convergence of algorithms. This book considers spaces that do not satisfy such compactness assumptions. In order to overcome these difficulties, the book uses the Baire category approach and considers approximate solutions. Therefore, it presents a number of new results concerning penalty methods in constrained optimization, existence of solutions in parametric optimization, well-posedness of vector minimization problems, and many other results obtained in the last ten years. The book is intended for mathematicians interested in optimization and applied functional analysis.
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.
Download or read book Metrics Norms Inner Products and Operator Theory written by Christopher Heil and published by Birkhäuser. This book was released on 2018-08-28 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is a self-contained introduction to the three main families that we encounter in analysis – metric spaces, normed spaces, and inner product spaces – and to the operators that transform objects in one into objects in another. With an emphasis on the fundamental properties defining the spaces, this book guides readers to a deeper understanding of analysis and an appreciation of the field as the “science of functions.” Many important topics that are rarely presented in an accessible way to undergraduate students are included, such as unconditional convergence of series, Schauder bases for Banach spaces, the dual of lp topological isomorphisms, the Spectral Theorem, the Baire Category Theorem, and the Uniform Boundedness Principle. The text is constructed in such a way that instructors have the option whether to include more advanced topics. Written in an appealing and accessible style, Metrics, Norms, Inner Products, and Operator Theory is suitable for independent study or as the basis for an undergraduate-level course. Instructors have several options for building a course around the text depending on the level and interests of their students. Key features: Aimed at students who have a basic knowledge of undergraduate real analysis. All of the required background material is reviewed in the first chapter. Suitable for undergraduate-level courses; no familiarity with measure theory is required. Extensive exercises complement the text and provide opportunities for learning by doing. A separate solutions manual is available for instructors via the Birkhäuser website (www.springer.com/978-3-319-65321-1). Unique text providing an undergraduate-level introduction to metrics, norms, inner products, and their associated operator theory.
Download or read book Introduction to the Analysis of Metric Spaces written by John R. Giles and published by Cambridge University Press. This book was released on 1987-09-03 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to the analysis of metric and normed linear spaces for undergraduate students in mathematics. Assuming a basic knowledge of real analysis and linear algebra, the student is exposed to the axiomatic method in analysis and is shown its power in exploiting the structure of fundamental analysis, which underlies a variety of applications. An example is the link between normed linear spaces and linear algebra; finite dimensional spaces are discussed early. The treatment progresses from the concrete to the abstract: thus metric spaces are studied in some detail before general topology is begun, though topological properties of metric spaces are explored in the book. Graded exercises are provided at the end of each section; in each set the earlier exercises are designed to assist in the detection of the structural properties in concrete examples while the later ones are more conceptually sophisticated.
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.
Download or read book Metric and normed spaces written by Andreĭ Nikolaevich Kolmogorov and published by . This book was released on 1957 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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:
Download or read book Functional Analysis written by Joseph Muscat and published by Springer Nature. This book was released on with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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.
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.
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.
Download or read book Probabilistic Metric Spaces written by B. Schweizer and published by Courier Corporation. This book was released on 2011-10-14 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This distinctly nonclassical treatment focuses on developing aspects that differ from the theory of ordinary metric spaces, working directly with probability distribution functions rather than random variables. The two-part treatment begins with an overview that discusses the theory's historical evolution, followed by a development of related mathematical machinery. The presentation defines all needed concepts, states all necessary results, and provides relevant proofs. The second part opens with definitions of probabilistic metric spaces and proceeds to examinations of special classes of probabilistic metric spaces, topologies, and several related structures, such as probabilistic normed and inner-product spaces. Throughout, the authors focus on developing aspects that differ from the theory of ordinary metric spaces, rather than simply transferring known metric space results to a more general setting.
Download or read book Metric and Normed Spaces written by A. N. Kolmogorov and published by . This book was released on 1957 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Metrics Norms And Integrals An Introduction To Contemporary Analysis written by Jerry J Koliha and published by World Scientific Publishing Company. This book was released on 2008-11-11 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Metrics, Norms and Integrals is a textbook on contemporary analysis based on the author's lectures given at the University of Melbourne for over two decades. It covers three main topics: metric and topological spaces, functional analysis, and the theory of the Lebesgue integral on measure spaces. This self-contained text contains a number of original presentations, including an early introduction of pseudometric spaces to motivate general topologies, an innovative introduction to the Lebesgue integral, and a discussion on the use of the Newton integral. It is thus a valuable book to inform and stimulate both undergraduate and graduate students.
Download or read book Multimedians in Metric and Normed Spaces written by E. R. Verheul and published by . This book was released on 1993 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:
