Advanced Functional Analysis
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Author |
: Eberhard Malkowsky |
Publisher |
: CRC Press |
Total Pages |
: 586 |
Release |
: 2019-02-25 |
ISBN-10 |
: 9780429809545 |
ISBN-13 |
: 0429809549 |
Rating |
: 4/5 (45 Downloads) |
Synopsis Advanced Functional Analysis by : Eberhard Malkowsky
Functional analysis and operator theory are widely used in the description, understanding and control of dynamical systems and natural processes in physics, chemistry, medicine and the engineering sciences. Advanced Functional Analysis is a self-contained and comprehensive reference for advanced functional analysis and can serve as a guide for related research. The book can be used as a textbook in advanced functional analysis, which is a modern and important field in mathematics, for graduate and postgraduate courses and seminars at universities. At the same time, it enables the interested readers to do their own research. Features Written in a concise and fluent style Covers a broad range of topics Includes related topics from research
Author |
: Eberhard Malkowsky |
Publisher |
: CRC Press |
Total Pages |
: 446 |
Release |
: 2019-02-25 |
ISBN-10 |
: 9780429809552 |
ISBN-13 |
: 0429809557 |
Rating |
: 4/5 (52 Downloads) |
Synopsis Advanced Functional Analysis by : Eberhard Malkowsky
Functional analysis and operator theory are widely used in the description, understanding and control of dynamical systems and natural processes in physics, chemistry, medicine and the engineering sciences. Advanced Functional Analysis is a self-contained and comprehensive reference for advanced functional analysis and can serve as a guide for related research. The book can be used as a textbook in advanced functional analysis, which is a modern and important field in mathematics, for graduate and postgraduate courses and seminars at universities. At the same time, it enables the interested readers to do their own research. Features Written in a concise and fluent style Covers a broad range of topics Includes related topics from research
Author |
: Theo Bühler |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 482 |
Release |
: 2018-08-08 |
ISBN-10 |
: 9781470441906 |
ISBN-13 |
: 147044190X |
Rating |
: 4/5 (06 Downloads) |
Synopsis Functional Analysis by : Theo Bühler
It begins in Chapter 1 with an introduction to the necessary foundations, including the Arzelà–Ascoli theorem, elementary Hilbert space theory, and the Baire Category Theorem. Chapter 2 develops the three fundamental principles of functional analysis (uniform boundedness, open mapping theorem, Hahn–Banach theorem) and discusses reflexive spaces and the James space. Chapter 3 introduces the weak and weak topologies and includes the theorems of Banach–Alaoglu, Banach–Dieudonné, Eberlein–Šmulyan, Kre&ibreve;n–Milman, as well as an introduction to topological vector spaces and applications to ergodic theory. Chapter 4 is devoted to Fredholm theory. It includes an introduction to the dual operator and to compact operators, and it establishes the closed image theorem. Chapter 5 deals with the spectral theory of bounded linear operators. It introduces complex Banach and Hilbert spaces, the continuous functional calculus for self-adjoint and normal operators, the Gelfand spectrum, spectral measures, cyclic vectors, and the spectral theorem. Chapter 6 introduces unbounded operators and their duals. It establishes the closed image theorem in this setting and extends the functional calculus and spectral measure to unbounded self-adjoint operators on Hilbert spaces. Chapter 7 gives an introduction to strongly continuous semigroups and their infinitesimal generators. It includes foundational results about the dual semigroup and analytic semigroups, an exposition of measurable functions with values in a Banach space, and a discussion of solutions to the inhomogeneous equation and their regularity properties. The appendix establishes the equivalence of the Lemma of Zorn and the Axiom of Choice, and it contains a proof of Tychonoff's theorem. With 10 to 20 elaborate exercises at the end of each chapter, this book can be used as a text for a one-or-two-semester course on functional analysis for beginning graduate students. Prerequisites are first-year analysis and linear algebra, as well as some foundational material from the second-year courses on point set topology, complex analysis in one variable, and measure and integration.
Author |
: Erwin Kreyszig |
Publisher |
: John Wiley & Sons |
Total Pages |
: 706 |
Release |
: 1991-01-16 |
ISBN-10 |
: 9780471504597 |
ISBN-13 |
: 0471504599 |
Rating |
: 4/5 (97 Downloads) |
Synopsis Introductory Functional Analysis with Applications by : Erwin Kreyszig
KREYSZIG The Wiley Classics Library consists of selected books originally published by John Wiley & Sons that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: Emil Artin Geometnc Algebra R. W. Carter Simple Groups Of Lie Type Richard Courant Differential and Integrai Calculus. Volume I Richard Courant Differential and Integral Calculus. Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics. Volume II Harold M. S. Coxeter Introduction to Modern Geometry. Second Edition Charles W. Curtis, Irving Reiner Representation Theory of Finite Groups and Associative Algebras Nelson Dunford, Jacob T. Schwartz unear Operators. Part One. General Theory Nelson Dunford. Jacob T. Schwartz Linear Operators, Part Two. Spectral Theory—Self Adjant Operators in Hilbert Space Nelson Dunford, Jacob T. Schwartz Linear Operators. Part Three. Spectral Operators Peter Henrici Applied and Computational Complex Analysis. Volume I—Power Senes-lntegrauon-Contormal Mapping-Locatvon of Zeros Peter Hilton, Yet-Chiang Wu A Course in Modern Algebra Harry Hochstadt Integral Equations Erwin Kreyszig Introductory Functional Analysis with Applications P. M. Prenter Splines and Variational Methods C. L. Siegel Topics in Complex Function Theory. Volume I —Elliptic Functions and Uniformizatton Theory C. L. Siegel Topics in Complex Function Theory. Volume II —Automorphic and Abelian Integrals C. L. Siegel Topics In Complex Function Theory. Volume III —Abelian Functions & Modular Functions of Several Variables J. J. Stoker Differential Geometry
Author |
: Kosaku Yosida |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 480 |
Release |
: 2013-04-17 |
ISBN-10 |
: 9783662117910 |
ISBN-13 |
: 3662117916 |
Rating |
: 4/5 (10 Downloads) |
Synopsis Functional Analysis by : Kosaku Yosida
Author |
: Daniel Alpay |
Publisher |
: Birkhäuser |
Total Pages |
: 523 |
Release |
: 2015-11-13 |
ISBN-10 |
: 9783319160597 |
ISBN-13 |
: 3319160591 |
Rating |
: 4/5 (97 Downloads) |
Synopsis An Advanced Complex Analysis Problem Book by : Daniel Alpay
This is an exercises book at the beginning graduate level, whose aim is to illustrate some of the connections between functional analysis and the theory of functions of one variable. A key role is played by the notions of positive definite kernel and of reproducing kernel Hilbert space. A number of facts from functional analysis and topological vector spaces are surveyed. Then, various Hilbert spaces of analytic functions are studied.
Author |
: Manfred Einsiedler |
Publisher |
: Springer |
Total Pages |
: 626 |
Release |
: 2017-11-21 |
ISBN-10 |
: 9783319585406 |
ISBN-13 |
: 3319585401 |
Rating |
: 4/5 (06 Downloads) |
Synopsis Functional Analysis, Spectral Theory, and Applications by : Manfred Einsiedler
This textbook provides a careful treatment of functional analysis and some of its applications in analysis, number theory, and ergodic theory. In addition to discussing core material in functional analysis, the authors cover more recent and advanced topics, including Weyl’s law for eigenfunctions of the Laplace operator, amenability and property (T), the measurable functional calculus, spectral theory for unbounded operators, and an account of Tao’s approach to the prime number theorem using Banach algebras. The book further contains numerous examples and exercises, making it suitable for both lecture courses and self-study. Functional Analysis, Spectral Theory, and Applications is aimed at postgraduate and advanced undergraduate students with some background in analysis and algebra, but will also appeal to everyone with an interest in seeing how functional analysis can be applied to other parts of mathematics.
Author |
: W. W. Sawyer |
Publisher |
: Courier Dover Publications |
Total Pages |
: 210 |
Release |
: 2010-12-22 |
ISBN-10 |
: 9780486478821 |
ISBN-13 |
: 0486478823 |
Rating |
: 4/5 (21 Downloads) |
Synopsis A First Look at Numerical Functional Analysis by : W. W. Sawyer
Functional analysis arose from traditional topics of calculus and integral and differential equations. This accessible text by an internationally renowned teacher and author starts with problems in numerical analysis and shows how they lead naturally to the concepts of functional analysis. Suitable for advanced undergraduates and graduate students, this book provides coherent explanations for complex concepts. Topics include Banach and Hilbert spaces, contraction mappings and other criteria for convergence, differentiation and integration in Banach spaces, the Kantorovich test for convergence of an iteration, and Rall's ideas of polynomial and quadratic operators. Numerous examples appear throughout the text.
Author |
: Martin Schechter |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 450 |
Release |
: 2001-11-13 |
ISBN-10 |
: 9780821828953 |
ISBN-13 |
: 0821828959 |
Rating |
: 4/5 (53 Downloads) |
Synopsis Principles of Functional Analysis by : Martin Schechter
This excellent book provides an elegant introduction to functional analysis ... carefully selected problems ... This is a nicely written book of great value for stimulating active work by students. It can be strongly recommended as an undergraduate or graduate text, or as a comprehensive book for self-study. --European Mathematical Society Newsletter Functional analysis plays a crucial role in the applied sciences as well as in mathematics. It is a beautiful subject that can be motivated and studied for its own sake. In keeping with this basic philosophy, the author has made this introductory text accessible to a wide spectrum of students, including beginning-level graduates and advanced undergraduates. The exposition is inviting, following threads of ideas, describing each as fully as possible, before moving on to a new topic. Supporting material is introduced as appropriate, and only to the degree needed. Some topics are treated more than once, according to the different contexts in which they arise. The prerequisites are minimal, requiring little more than advanced calculus and no measure theory. The text focuses on normed vector spaces and their important examples, Banach spaces and Hilbert spaces. The author also includes topics not usually found in texts on the subject. This Second Edition incorporates many new developments while not overshadowing the book's original flavor. Areas in the book that demonstrate its unique character have been strengthened. In particular, new material concerning Fredholm and semi-Fredholm operators is introduced, requiring minimal effort as the necessary machinery was already in place. Several new topics are presented, but relate to only those concepts and methods emanating from other parts of the book. These topics include perturbation classes, measures of noncompactness, strictly singular operators, and operator constants. Overall, the presentation has been refined, clarified, and simplified, and many new problems have been added. The book is recommended to advanced undergraduates, graduate students, and pure and applied research mathematicians interested in functional analysis and operator theory.
Author |
: Vladimir Kadets |
Publisher |
: Springer |
Total Pages |
: 553 |
Release |
: 2018-07-10 |
ISBN-10 |
: 9783319920047 |
ISBN-13 |
: 3319920049 |
Rating |
: 4/5 (47 Downloads) |
Synopsis A Course in Functional Analysis and Measure Theory by : Vladimir Kadets
Written by an expert on the topic and experienced lecturer, this textbook provides an elegant, self-contained introduction to functional analysis, including several advanced topics and applications to harmonic analysis. Starting from basic topics before proceeding to more advanced material, the book covers measure and integration theory, classical Banach and Hilbert space theory, spectral theory for bounded operators, fixed point theory, Schauder bases, the Riesz-Thorin interpolation theorem for operators, as well as topics in duality and convexity theory. Aimed at advanced undergraduate and graduate students, this book is suitable for both introductory and more advanced courses in functional analysis. Including over 1500 exercises of varying difficulty and various motivational and historical remarks, the book can be used for self-study and alongside lecture courses.