Lectures On Functional Analysis And The Lebesgue Integral

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Lectures on Functional Analysis and the Lebesgue Integral

Author : Vilmos Komornik
Publisher : Springer
ISBN 13 : 1447168119
Total Pages : 403 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Lectures on Functional Analysis and the Lebesgue Integral by : Vilmos Komornik

Download or read book Lectures on Functional Analysis and the Lebesgue Integral written by Vilmos Komornik and published by Springer. This book was released on 2016-06-03 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook, based on three series of lectures held by the author at the University of Strasbourg, presents functional analysis in a non-traditional way by generalizing elementary theorems of plane geometry to spaces of arbitrary dimension. This approach leads naturally to the basic notions and theorems. Most results are illustrated by the small lp spaces. The Lebesgue integral, meanwhile, is treated via the direct approach of Frigyes Riesz, whose constructive definition of measurable functions leads to optimal, clear-cut versions of the classical theorems of Fubini-Tonelli and Radon-Nikodým. Lectures on Functional Analysis and the Lebesgue Integral presents the most important topics for students, with short, elegant proofs. The exposition style follows the Hungarian mathematical tradition of Paul Erdős and others. The order of the first two parts, functional analysis and the Lebesgue integral, may be reversed. In the third and final part they are combined to study various spaces of continuous and integrable functions. Several beautiful, but almost forgotten, classical theorems are also included. Both undergraduate and graduate students in pure and applied mathematics, physics and engineering will find this textbook useful. Only basic topological notions and results are used and various simple but pertinent examples and exercises illustrate the usefulness and optimality of most theorems. Many of these examples are new or difficult to localize in the literature, and the original sources of most notions and results are indicated to help the reader understand the genesis and development of the field.

Lectures on Functional Analysis and Applications

Author : Vladimir Semenovich Pugachev
Publisher : World Scientific
ISBN 13 : 9789810237233
Total Pages : 756 pages
Book Rating : 4.2/5 (372 download)

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Book Synopsis Lectures on Functional Analysis and Applications by : Vladimir Semenovich Pugachev

Download or read book Lectures on Functional Analysis and Applications written by Vladimir Semenovich Pugachev and published by World Scientific. This book was released on 1999 with total page 756 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for those having only a moderate background in mathematics, who need to increase their mathematical knowledge for development in their areas of work and to read the related mathematical literature. The material covered, which includes practically all the information on functional analysis that may be necessary for those working in various areas of applications of mathematics, as well as the simplicity of presentation, differentiates this book from others. About 300 examples and more than 500 problems are provided to help readers understand and master the theories presented. The list of references enables readers to explore those topics in which they are interested, and gather further information about applications used as examples in the book.Applications: Probability Theory and Statistics, Signal and Image Processing, Systems Analysis and Design.

Metrics, Norms and Integrals

Author : J J Koliha
Publisher : World Scientific Publishing Company
ISBN 13 : 9813101180
Total Pages : 428 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Metrics, Norms and Integrals by : J J Koliha

Download or read book Metrics, Norms and Integrals written by J J Koliha and published by World Scientific Publishing Company. This book was released on 2008-11-11 with total page 428 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.

Lectures on Functional Analysis and Applications

Author : V S Pugachev
Publisher : World Scientific Publishing Company
ISBN 13 : 9813102926
Total Pages : 752 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Lectures on Functional Analysis and Applications by : V S Pugachev

Download or read book Lectures on Functional Analysis and Applications written by V S Pugachev and published by World Scientific Publishing Company. This book was released on 1999-07-26 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for those having only a moderate background in mathematics, who need to increase their mathematical knowledge for development in their areas of work and to read the related mathematical literature. The material covered, which includes practically all the information on functional analysis that may be necessary for those working in various areas of applications of mathematics, as well as the simplicity of presentation, differentiates this book from others. About 300 examples and more than 500 problems are provided to help readers understand and master the theories presented. The list of references enables readers to explore those topics in which they are interested, and gather further information about applications used as examples in the book. Applications: Probability Theory and Statistics, Signal and Image Processing, Systems Analysis and Design.

Metrics, Norms and Integrals

Author : J. J. Koliha
Publisher : World Scientific Publishing Company Incorporated
ISBN 13 : 9789812836571
Total Pages : 408 pages
Book Rating : 4.8/5 (365 download)

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Book Synopsis Metrics, Norms and Integrals by : J. J. Koliha

Download or read book Metrics, Norms and Integrals written by J. J. Koliha and published by World Scientific Publishing Company Incorporated. This book was released on 2008 with total page 408 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.

Functional Analysis

Author : Elias M. Stein
Publisher : Princeton University Press
ISBN 13 : 1400840554
Total Pages : 442 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Functional Analysis by : Elias M. Stein

Download or read book Functional Analysis written by Elias M. Stein and published by Princeton University Press. This book was released on 2011-08-22 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fourth and final volume in the Princeton Lectures in Analysis, a series of textbooks that aim to present, in an integrated manner, the core areas of analysis. Beginning with the basic facts of functional analysis, this volume looks at Banach spaces, Lp spaces, and distribution theory, and highlights their roles in harmonic analysis. The authors then use the Baire category theorem to illustrate several points, including the existence of Besicovitch sets. The second half of the book introduces readers to other central topics in analysis, such as probability theory and Brownian motion, which culminates in the solution of Dirichlet's problem. The concluding chapters explore several complex variables and oscillatory integrals in Fourier analysis, and illustrate applications to such diverse areas as nonlinear dispersion equations and the problem of counting lattice points. Throughout the book, the authors focus on key results in each area and stress the organic unity of the subject. A comprehensive and authoritative text that treats some of the main topics of modern analysis A look at basic functional analysis and its applications in harmonic analysis, probability theory, and several complex variables Key results in each area discussed in relation to other areas of mathematics Highlights the organic unity of large areas of analysis traditionally split into subfields Interesting exercises and problems illustrate ideas Clear proofs provided

Measure, Integration and Function Spaces

Author : Charles Swartz
Publisher : World Scientific
ISBN 13 : 9789810216108
Total Pages : 300 pages
Book Rating : 4.2/5 (161 download)

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Book Synopsis Measure, Integration and Function Spaces by : Charles Swartz

Download or read book Measure, Integration and Function Spaces written by Charles Swartz and published by World Scientific. This book was released on 1994 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text contains a basic introduction to the abstract measure theory and the Lebesgue integral. Most of the standard topics in the measure and integration theory are discussed. In addition, topics on the Hewitt-Yosida decomposition, the Nikodym and Vitali-Hahn-Saks theorems and material on finitely additive set functions not contained in standard texts are explored. There is an introductory section on functional analysis, including the three basic principles, which is used to discuss many of the classic Banach spaces of functions and their duals. There is also a chapter on Hilbert space and the Fourier transform.

The Integral

Author : Steven G. Krantz
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1608456137
Total Pages : 106 pages
Book Rating : 4.6/5 (84 download)

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Book Synopsis The Integral by : Steven G. Krantz

Download or read book The Integral written by Steven G. Krantz and published by Morgan & Claypool Publishers. This book was released on 2011 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats all of the most commonly used theories of the integral. After motivating the idea of integral, we devote a full chapter to the Riemann integral and the next to the Lebesgue integral. Another chapter compares and contrasts the two theories. The concluding chapter offers brief introductions to the Henstock integral, the Daniell integral, the Stieltjes integral, and other commonly used integrals. The purpose of this book is to provide a quick but accurate (and detailed) introduction to all aspects of modern integration theory. It should be accessible to any student who has had calculus and some exposure to upper division mathematics. Table of Contents: Introduction / The Riemann Integral / The Lebesgue Integral / Comparison of the Riemann and Lebesgue Integrals / Other Theories of the Integral

Real Analysis

Author : Elias M. Stein
Publisher : Princeton University Press
ISBN 13 : 1400835569
Total Pages : 423 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Real Analysis by : Elias M. Stein

Download or read book Real Analysis written by Elias M. Stein and published by Princeton University Press. This book was released on 2009-11-28 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. After setting forth the basic facts of measure theory, Lebesgue integration, and differentiation on Euclidian spaces, the authors move to the elements of Hilbert space, via the L2 theory. They next present basic illustrations of these concepts from Fourier analysis, partial differential equations, and complex analysis. The final part of the book introduces the reader to the fascinating subject of fractional-dimensional sets, including Hausdorff measure, self-replicating sets, space-filling curves, and Besicovitch sets. Each chapter has a series of exercises, from the relatively easy to the more complex, that are tied directly to the text. A substantial number of hints encourage the reader to take on even the more challenging exercises. As with the other volumes in the series, Real Analysis is accessible to students interested in such diverse disciplines as mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels. Also available, the first two volumes in the Princeton Lectures in Analysis:

Lectures on Measure and Integration

Author : Harold Widom
Publisher : Courier Dover Publications
ISBN 13 : 0486810283
Total Pages : 177 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Lectures on Measure and Integration by : Harold Widom

Download or read book Lectures on Measure and Integration written by Harold Widom and published by Courier Dover Publications. This book was released on 2016-11-16 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: These well-known and concise lecture notes present the fundamentals of the Lebesgue theory of integration and an introduction to some of the theory's applications. Suitable for advanced undergraduates and graduate students of mathematics, the treatment also covers topics of interest to practicing analysts. Author Harold Widom emphasizes the construction and properties of measures in general and Lebesgue measure in particular as well as the definition of the integral and its main properties. The notes contain chapters on the Lebesgue spaces and their duals, differentiation of measures in Euclidean space, and the application of integration theory to Fourier series.

Lectures on the Theory of Integration

Author : Ralph Henstock
Publisher : World Scientific
ISBN 13 : 9789971504519
Total Pages : 224 pages
Book Rating : 4.5/5 (45 download)

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Book Synopsis Lectures on the Theory of Integration by : Ralph Henstock

Download or read book Lectures on the Theory of Integration written by Ralph Henstock and published by World Scientific. This book was released on 1988 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to be self-contained, giving the theory of absolute (equivalent to Lebesgue) and non-absolute (equivalent to Denjoy-Perron) integration by using a simple extension of the Riemann integral. A useful tool for mathematicians and scientists needing advanced integration theory would be a method combining the ideas of the calculus of indefinite integral and Riemann definite integral in such a way that Lebesgue properties can be proved easily.Three important results that have not appeared in any other book distinguish this book from the rest. First a result on limits of sequences under the integral sign, secondly the necessary and sufficient conditions for the various limits under the integral sign and thirdly the application of these results to ordinary differential equations. The present book will give non-absolute integration theory just as easily as the absolute theory, and Stieltjes-type integration too.

Linear Functional Analysis

Author : Bernard Epstein
Publisher :
ISBN 13 :
Total Pages : 248 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Linear Functional Analysis by : Bernard Epstein

Download or read book Linear Functional Analysis written by Bernard Epstein and published by . This book was released on 1970 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lectures In Nonlinear Functional Analysis: Synopsis Of Lectures Given At The Faculty Of Physics Of Lomonosov Moscow State University

Download Lectures In Nonlinear Functional Analysis: Synopsis Of Lectures Given At The Faculty Of Physics Of Lomonosov Moscow State University PDF Online Free

Author : Maxim Olegovich Korpusov
Publisher : World Scientific
ISBN 13 : 981124894X
Total Pages : 377 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Lectures In Nonlinear Functional Analysis: Synopsis Of Lectures Given At The Faculty Of Physics Of Lomonosov Moscow State University by : Maxim Olegovich Korpusov

Download or read book Lectures In Nonlinear Functional Analysis: Synopsis Of Lectures Given At The Faculty Of Physics Of Lomonosov Moscow State University written by Maxim Olegovich Korpusov and published by World Scientific. This book was released on 2021-12-28 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a systematic presentation of basic notions, facts, and ideas of nonlinear functional analysis and their applications to nonlinear partial differential equations. It begins from a brief introduction to linear functional analysis, including various types of convergence and functional spaces. The main part of the book is devoted to the theory of nonlinear operators. Various methods of the study of nonlinear differential equations based on the facts of nonlinear analysis are presented in detail. This book may serve as an introductory textbook for students and undergraduates specializing in modern mathematical physics.

Functional Analysis with Applications

Author : Svetlin G. Georgiev
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110657724
Total Pages : 402 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Functional Analysis with Applications by : Svetlin G. Georgiev

Download or read book Functional Analysis with Applications written by Svetlin G. Georgiev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-06-17 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on functional analysis covers all the basics of the subject (normed, Banach and Hilbert spaces, Lebesgue integration and spaces, linear operators and functionals, compact and self-adjoint operators, small parameters, fixed point theory) with a strong focus on examples, exercises and practical problems, thus making it ideal as course material but also as a reference for self-study.

Real and Functional Analysis

Author : Vladimir I. Bogachev
Publisher : Springer Nature
ISBN 13 : 3030382192
Total Pages : 586 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Real and Functional Analysis by : Vladimir I. Bogachev

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.

A (Terse) Introduction to Lebesgue Integration

Author : John M. Franks
Publisher : American Mathematical Soc.
ISBN 13 : 0821848623
Total Pages : 219 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis A (Terse) Introduction to Lebesgue Integration by : John M. Franks

Download or read book A (Terse) Introduction to Lebesgue Integration written by John M. Franks and published by American Mathematical Soc.. This book was released on 2009 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a student's first encounter with the concepts of measure theory and functional analysis. This book reflects the belief that difficult concepts should be introduced in their simplest and most concrete forms. It is suitable for an advanced undergraduate course or for the start of a graduate course.

Lectures and Exercises on Functional Analysis

Author : Александр Яковлевич Хелемский
Publisher : American Mathematical Soc.
ISBN 13 : 9780821889695
Total Pages : 496 pages
Book Rating : 4.8/5 (896 download)

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Book Synopsis Lectures and Exercises on Functional Analysis by : Александр Яковлевич Хелемский

Download or read book Lectures and Exercises on Functional Analysis written by Александр Яковлевич Хелемский and published by American Mathematical Soc.. This book was released on with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is based on courses taught by the author at Moscow State University. Compared to many other books on the subject, it is unique in that the exposition is based on extensive use of the language and elementary constructions of category theory. Among topics featured in the book are the theory of Banach and Hilbert tensor products, the theory of distributions and weak topologies, and Borel operator calculus. The book contains many examples illustrating the general theory presented, as well as multiple exercises that help the reader to learn the subject. It can be used as a textbook on selected topics of functional analysis and operator theory. Prerequisites include linear algebra, elements of real analysis, and elements of the theory of metric spaces.