Problems In Real And Functional Analysis
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Problems In Real And Functional Analysis
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Author : Alberto Torchinsky
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-12-14
Problems In Real And Functional Analysis written by Alberto Torchinsky and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-14 with Functional analysis categories.
It is generally believed that solving problems is the most important part of the learning process in mathematics because it forces students to truly understand the definitions, comb through the theorems and proofs, and think at length about the mathematics. The purpose of this book is to complement the existing literature in introductory real and functional analysis at the graduate level with a variety of conceptual problems (1,457 in total), ranging from easily accessible to thought provoking, mixing the practical and the theoretical aspects of the subject. Problems are grouped into ten chapters covering the main topics usually taught in courses on real and functional analysis. Each of these chapters opens with a brief reader's guide stating the needed definitions and basic results in the area and closes with a short description of the problems. - See more at: http://bookstore.ams.org/GSM-166/#sthash.ZMb1J6lg.dpuf It is generally believed that solving problems is the most important part of the learning process in mathematics because it forces students to truly understand the definitions, comb through the theorems and proofs, and think at length about the mathematics. The purpose of this book is to complement the existing literature in introductory real and functional analysis at the graduate level with a variety of conceptual problems (1,457 in total), ranging from easily accessible to thought provoking, mixing the practical and the theoretical aspects of the subject. Problems are grouped into ten chapters covering the main topics usually taught in courses on real and functional analysis. Each of these chapters opens with a brief reader's guide stating the needed definitions and basic results in the area and closes with a short description of the problems. The Problem chapters are accompanied by Solution chapters, which include solutions to two-thirds of the problems. Students can expect the solutions to be written in a direct language that they can understand; usually the most "natural" rather than the most elegant solution is presented. The Problem chapters are accompanied by Solution chapters, which include solutions to two-thirds of the problems. Students can expect the solutions to be written in a direct language that they can understand; usually the most “natural” rather than the most elegant solution is presented. - See more at: http://bookstore.ams.org/GSM-166/#sthash.ZMb1J6lg.dpufhe Problem chapters are accompanied by Solution chapters, which include solutions to two-thirds of the - See more at: http://bookstore.ams.org/GSM-166/#sthash.ZMb1J6lg.dpuft is generally believed that solving problems is the most important part of the learning process in mathematics because it forces students to truly understand the definitions, comb through the theorems and proofs, and think at length about the mathematics. The purpose of this book is to complement the existing literature in introductory real and functional analysis at the graduate level with a variety of - See more at: http://bookstore.ams.org/GSM-166/#sthash.ZMb1J6lg.dpufIt is generally believed that solving problems is the most important part of the learning process in mathematics because it forces students to truly understand the definitions, comb through the theorems and proofs, and think at length about the mathematics. The purpose of this book is to complement the existing literature in introductory real and functional analysis at the graduate level with a variety of conceptual problems (1,457 in total), ranging from easily accessible to thought provoking, mixing the practical and the theoretical aspects of the subject. Problems are grouped into ten chapters covering the main topics usually taught in courses on real and functional analysis. Each of these chapters opens with a brief reader's guide stating - See more at: http://bookstore.ams.org/GSM-166/#sthash.ZMb1J6lg.dpuf
Problems In Real And Functional Analysis
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Author : Alberto Torchinsky
language : en
Publisher:
Release Date : 2015
Problems In Real And Functional Analysis written by Alberto Torchinsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Functional analysis categories.
Cover -- Title page -- Dedication -- Contents -- Preface -- Part 1. Problems -- Chapter 1. Set theory and metric spaces -- Chapter 2. Measures -- Chapter 3. Lebesgue measure -- Chapter 4. Measurable and integrable functions -- Chapter 5. ^{ } spaces -- Chapter 6. Sequences of functions -- Chapter 7. Product measures -- Chapter 8. Normed linear spaces. Functionals -- Chapter 9. Normed linear spaces. Linear operators -- Chapter 10. Hilbert spaces -- Part 2. Solutions -- Chapter 11. Set theory and metric spaces -- Chapter 12. Measures -- Chapter 13. Lebesgue measure -- Chapter 14. Measurable and integrable functions -- Chapter 15. ^{ } spaces -- Chapter 16. Sequences of functions -- Chapter 17. Product measures -- Chapter 18. Normed linear spaces. Functionals -- Chapter 19. Normed linear spaces. Linear operators -- Chapter 20. Hilbert spaces -- Index -- Back Cover
Theorems And Problems In Functional Analysis
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Author : A. A. Kirillov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Theorems And Problems In Functional Analysis written by A. A. Kirillov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Even the simplest mathematical abstraction of the phenomena of reality the real line-can be regarded from different points of view by different mathematical disciplines. For example, the algebraic approach to the study of the real line involves describing its properties as a set to whose elements we can apply" operations," and obtaining an algebraic model of it on the basis of these properties, without regard for the topological properties. On the other hand, we can focus on the topology of the real line and construct a formal model of it by singling out its" continuity" as a basis for the model. Analysis regards the line, and the functions on it, in the unity of the whole system of their algebraic and topological properties, with the fundamental deductions about them obtained by using the interplay between the algebraic and topological structures. The same picture is observed at higher stages of abstraction. Algebra studies linear spaces, groups, rings, modules, and so on. Topology studies structures of a different kind on arbitrary sets, structures that give mathe matical meaning to the concepts of a limit, continuity, a neighborhood, and so on. Functional analysis takes up topological linear spaces, topological groups, normed rings, modules of representations of topological groups in topological linear spaces, and so on. Thus, the basic object of study in functional analysis consists of objects equipped with compatible algebraic and topological structures.
Problems In Mathematical Analysis
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Author : Biler
language : en
Publisher: Routledge
Release Date : 2017-10-19
Problems In Mathematical Analysis written by Biler and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-19 with Mathematics categories.
Chapter 1 poses 134 problems concerning real and complex numbers, chapter 2 poses 123 problems concerning sequences, and so it goes, until in chapter 9 one encounters 201 problems concerning functional analysis. The remainder of the book is given over to the presentation of hints, answers or referen
Nonlinearity And Functional Analysis
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Author : Melvyn S. Berger
language : en
Publisher: Academic Press
Release Date : 1977-10-27
Nonlinearity And Functional Analysis written by Melvyn S. Berger and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-10-27 with Mathematics categories.
Nonlinearity and Functional Analysis is a collection of lectures that aim to present a systematic description of fundamental nonlinear results and their applicability to a variety of concrete problems taken from various fields of mathematical analysis. For decades, great mathematical interest has focused on problems associated with linear operators and the extension of the well-known results of linear algebra to an infinite-dimensional context. This interest has been crowned with deep insights, and the substantial theory that has been developed has had a profound influence throughout the mathematical sciences. This volume comprises six chapters and begins by presenting some background material, such as differential-geometric sources, sources in mathematical physics, and sources from the calculus of variations, before delving into the subject of nonlinear operators. The following chapters then discuss local analysis of a single mapping and parameter dependent perturbation phenomena before going into analysis in the large. The final chapters conclude the collection with a discussion of global theories for general nonlinear operators and critical point theory for gradient mappings. This book will be of interest to practitioners in the fields of mathematics and physics, and to those with interest in conventional linear functional analysis and ordinary and partial differential equations.
Exercises In Functional Analysis
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Author : C. Costara
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Exercises In Functional Analysis written by C. Costara and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
This book contains almost 450 exercises, all with complete solutions; it provides supplementary examples, counter-examples, and applications for the basic notions usually presented in an introductory course in Functional Analysis. Three comprehensive sections cover the broad topic of functional analysis. A large number of exercises on the weak topologies is included.
Applied Functional Analysis
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Author : Abul Hasan Siddiqi
language : en
Publisher: CRC Press
Release Date : 2003-09-19
Applied Functional Analysis written by Abul Hasan Siddiqi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-19 with Mathematics categories.
The methods of functional analysis have helped solve diverse real-world problems in optimization, modeling, analysis, numerical approximation, and computer simulation. Applied Functional Analysis presents functional analysis results surfacing repeatedly in scientific and technological applications and presides over the most current analytical and n
Problems In Real And Complex Analysis
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Author : Bernard R. Gelbaum
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Problems In Real And Complex Analysis written by Bernard R. Gelbaum and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This text covers many principal topics in the theory of functions of a complex variable. These include, in real analysis, set algebra, measure and topology, real- and complex-valued functions, and topological vector spaces. In complex analysis, they include polynomials and power series, functions holomorphic in a region, entire functions, analytic continuation, singularities, harmonic functions, families of functions, and convexity theorems.
Principles Of Real Analysis
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Author : Charalambos D. Aliprantis
language : en
Publisher: Gulf Professional Publishing
Release Date : 1998-08-26
Principles Of Real Analysis written by Charalambos D. Aliprantis and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-08-26 with Mathematics categories.
The new, Third Edition of this successful text covers the basic theory of integration in a clear, well-organized manner. The authors present an imaginative and highly practical synthesis of the "Daniell method" and the measure theoretic approach. It is the ideal text for undergraduate and first-year graduate courses in real analysis. This edition offers a new chapter on Hilbert Spaces and integrates over 150 new exercises. New and varied examples are included for each chapter. Students will be challenged by the more than 600 exercises. Topics are treated rigorously, illustrated by examples, and offer a clear connection between real and functional analysis. This text can be used in combination with the authors' Problems in Real Analysis, 2nd Edition, also published by Academic Press, which offers complete solutions to all exercises in the Principles text. Key Features: * Gives a unique presentation of integration theory * Over 150 new exercises integrated throughout the text * Presents a new chapter on Hilbert Spaces * Provides a rigorous introduction to measure theory * Illustrated with new and varied examples in each chapter * Introduces topological ideas in a friendly manner * Offers a clear connection between real analysis and functional analysis * Includes brief biographies of mathematicians "All in all, this is a beautiful selection and a masterfully balanced presentation of the fundamentals of contemporary measure and integration theory which can be grasped easily by the student." --J. Lorenz in Zentralblatt für Mathematik "...a clear and precise treatment of the subject. There are many exercises of varying degrees of difficulty. I highly recommend this book for classroom use." --CASPAR GOFFMAN, Department of Mathematics, Purdue University
Real And Functional Analysis
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Author : Vladimir I. Bogachev
language : en
Publisher: Springer Nature
Release Date : 2020-02-25
Real And Functional Analysis written by Vladimir I. Bogachev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-25 with Mathematics categories.
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.