Mathematical Analysis Elementary Functional Analysis
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Elementary Functional Analysis
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Author : Georgi E. Shilov
language : en
Publisher: Courier Corporation
Release Date : 2013-04-15
Elementary Functional Analysis written by Georgi E. Shilov and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-15 with Mathematics categories.
Introductory text covers basic structures of mathematical analysis (linear spaces, metric spaces, normed linear spaces, etc.), differential equations, orthogonal expansions, Fourier transforms, and more. Includes problems with hints and answers. Bibliography. 1974 edition.
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 : 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. ContentsPreliminariesMetric SpacesNormed Vector and Banach SpacesInner Product and Hilbert SpacesLinear Operators and FunctionalsThree Fundamental Principles of Linear Functional AnalysisDuality and ReflexivityThe Axiom of Choice and Equivalents
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 : Charles Swartz
language : en
Publisher: World Scientific Publishing Company
Release Date : 2009-07-13
Elementary Functional Analysis written by Charles 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 Science 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.
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.
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.
Analysis I
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Author : Roger Godement
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Analysis I written by Roger Godement 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.
Functions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes. Based on a course given by the author to large audiences at Paris VII University for many years, the exposition proceeds somewhat nonlinearly, blending rigorous mathematics skilfully with didactical and historical considerations. It sets out to illustrate the variety of possible approaches to the main results, in order to initiate the reader to methods, the underlying reasoning, and fundamental ideas. It is suitable for both teaching and self-study. In his familiar, personal style, the author emphasizes ideas over calculations and, avoiding the condensed style frequently found in textbooks, explains these ideas without parsimony of words. The French edition in four volumes, published from 1998, has met with resounding success: the first two volumes are now available in English.
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.