Elementary Functional Analysis
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Elementary Functional Analysis
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Author : Barbara MacCluer
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-20
Elementary Functional Analysis written by Barbara MacCluer 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 2008-10-20 with Mathematics categories.
Functional analysis arose in the early twentieth century and gradually, conquering one stronghold after another, became a nearly universal mathematical doctrine, not merely a new area of mathematics, but a new mathematical world view. Its appearance was the inevitable consequence of the evolution of all of nineteenth-century mathematics, in particular classical analysis and mathematical physics. Its original basis was formed by Cantor’s theory of sets and linear algebra. Its existence answered the question of how to state general principles of a broadly interpreted analysis in a way suitable for the most diverse situations. A.M. Vershik ([45], p. 438). This text evolved from the content of a one semester introductory course in fu- tional analysis that I have taught a number of times since 1996 at the University of Virginia. My students have included ?rst and second year graduate students prep- ing for thesis work in analysis, algebra, or topology, graduate students in various departments in the School of Engineering and Applied Science, and several und- graduate mathematics or physics majors. After a ?rst draft of the manuscript was completed, it was also used for an independent reading course for several und- graduates preparing for graduate school.
Elementary Functional Analysis
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Author : Georgi Eugen Shilov (Mathématicien.)
language : en
Publisher:
Release Date : 1974
Elementary Functional Analysis written by Georgi Eugen Shilov (Mathématicien.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with categories.
Elementary Functional Analysis
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Author : Georgii Evgen'evich Shilov
language : en
Publisher:
Release Date : 1974
Elementary Functional Analysis written by Georgii Evgen'evich Shilov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Functional analysis categories.
Elementary Functional Analysis
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Author : Marat V. Markin
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-10-08
Elementary Functional Analysis written by Marat V. Markin and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-08 with Mathematics categories.
While there is a plethora of excellent, but mostly "tell-it-all'' books on the subject, this one is intended to take a unique place in what today seems to be a still wide open niche for an introductory text on the basics of functional analysis to be taught within the existing constraints of the standard, for the United States, one-semester graduate curriculum (fifteen weeks with two seventy-five-minute lectures per week). The book consists of seven chapters and an appendix taking the reader from the fundamentals of abstract spaces (metric, vector, normed vector, and inner product), through the basics of linear operators and functionals, the three fundamental principles (the Hahn-Banach Theorem, the Uniform Boundedness Principle, the Open Mapping Theorem and its equivalents: the Inverse Mapping and Closed Graph Theorems) with their numerous profound implications and certain interesting applications, to the elements of the duality and reflexivity theory. Chapter 1 outlines some necessary preliminaries, while the Appendix gives a concise discourse on the celebrated Axiom of Choice, its equivalents (the Hausdorff Maximal Principle, Zorn's Lemma, and Zermello's Well-Ordering Principle), and ordered sets. Being designed as a text to be used in a classroom, the book constantly calls for the student's actively mastering the knowledge of the subject matter. It contains 112 Problems, which are indispensable for understanding and moving forward. Many important statements are given as problems, a lot of these are frequently referred to and used in the main body. There are also 376 Exercises throughout the text, including Chapter 1 and the Appendix, which require of the student to prove or verify a statement or an example, fill in necessary details in a proof, or provide an intermediate step or a counterexample. They are also an inherent part of the material. More difficult problems are marked with an asterisk, many problem and exercises being supplied with "existential'' hints. The book is generous on Examples and contains numerous Remarks accompanying every definition and virtually each statement to discuss certain subtleties, raise questions on whether the converse assertions are true, whenever appropriate, or whether the conditions are essential. The prerequisites are set intentionally quite low, the students not being assumed to have taken graduate courses in real or complex analysis and general topology, to make the course accessible and attractive to a wider audience of STEM (science, technology, engineering, and mathematics) graduate students or advanced undergraduates with a solid background in calculus and linear algebra. With proper attention given to applications, plenty of examples, problems, and exercises, this well-designed text is ideal for a one-semester graduate course on the fundamentals of functional analysis for students in mathematics, physics, computer science, and engineering. Contents Preliminaries Metric Spaces Normed Vector and Banach Spaces Inner Product and Hilbert Spaces Linear Operators and Functionals Three Fundamental Principles of Linear Functional Analysis Duality and Reflexivity The Axiom of Choice and Equivalents
Elementary Functional Analysis
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Author :
language : en
Publisher:
Release Date : 1974
Elementary Functional Analysis written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with categories.
Functional Analysis
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Author : Markus Haase
language : en
Publisher: American Mathematical Society
Release Date : 2014-09-17
Functional Analysis written by Markus Haase and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-17 with Mathematics categories.
This book introduces functional analysis at an elementary level without assuming any background in real analysis, for example on metric spaces or Lebesgue integration. It focuses on concepts and methods relevant in applied contexts such as variational methods on Hilbert spaces, Neumann series, eigenvalue expansions for compact self-adjoint operators, weak differentiation and Sobolev spaces on intervals, and model applications to differential and integral equations. Beyond that, the final chapters on the uniform boundedness theorem, the open mapping theorem and the Hahn-Banach theorem provide a stepping-stone to more advanced texts. The exposition is clear and rigorous, featuring full and detailed proofs. Many examples illustrate the new notions and results. Each chapter concludes with a large collection of exercises, some of which are referred to in the margin of the text, tailor-made in order to guide the student digesting the new material. Optional sections and chapters supplement the mandatory parts and allow for modular teaching spanning from basic to honors track level.
Elementary Functional Analysis
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Author : Charles W Swartz
language : en
Publisher: World Scientific Publishing Company
Release Date : 2009-07-13
Elementary Functional Analysis written by Charles W Swartz and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-13 with Mathematics categories.
This text is an introduction to functional analysis which requires readers to have a minimal background in linear algebra and real analysis at the first-year graduate level. Prerequisite knowledge of general topology or Lebesgue integration is not required. The book explains the principles and applications of functional analysis and explores the development of the basic properties of normed linear, inner product spaces and continuous linear operators defined in these spaces. Though Lebesgue integral is not discussed, the book offers an in-depth knowledge on the numerous applications of the abstract results of functional analysis in differential and integral equations, Banach limits, harmonic analysis, summability and numerical integration. Also covered in the book are versions of the spectral theorem for compact, symmetric operators and continuous, self adjoint operators.
Mathematical Analysis
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Author : G.E. Shilov
language : en
Publisher:
Release Date : 1974
Mathematical Analysis written by G.E. Shilov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with categories.
Mathematical Analysis Elementary Functional Analysis
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Author : Georgiĭ Evgenʹevich Shilov
language : en
Publisher:
Release Date : 1973
Mathematical Analysis Elementary Functional Analysis written by Georgiĭ Evgenʹevich Shilov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Mathematical analysis categories.
Elementary Functional Analysis Engl
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Author : Georgij E. Šilov
language : en
Publisher:
Release Date : 1974
Elementary Functional Analysis Engl written by Georgij E. Šilov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with categories.