Functional Analysis And Its Applications

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Functional Analysis

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Author : Leonid P. Lebedev
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-29

Functional Analysis written by Leonid P. Lebedev 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 2006-04-29 with Mathematics categories.

This book started its life as a series of lectures given by the second author from the 1970’s onwards to students in their third and fourth years in the Department of Mechanics and Mathematics at Rostov State University. For these lectures there was also an audience of engineers and applied mechanicists who wished to understand the functional analysis used in contemporary research in their fields. These people were not so much interested in functional analysis itself as in its applications; they did not want to be told about functional analysis in its most abstract form, but wanted a guided tour through those parts of the analysis needed for their applications. The lecture notes evolved over the years as the first author started to make more formal typewritten versions incorporating new material. About 1990 the first author prepared an English version and submitted it to Kluwer Academic Publishers for inclusion in the series Solid Mechanics and its Applications. At that state the notes were divided into three long chapters covering linear and nonlinear analysis. As Series Editor, the third author started to edit them. The requirements of lecture notes and books are vastly different. A book has to be complete (in some sense), self contained, and able to be read without the help of an instructor.

Functional Analysis

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Author : R.E. Edwards
language : en
Publisher: Courier Corporation
Release Date : 2012-10-25

Functional Analysis written by R.E. Edwards and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-25 with Mathematics categories.

"The book contains an enormous amount of information — mathematical, bibliographical and historical — interwoven with some outstanding heuristic discussions." — Mathematical Reviews. In this massive graduate-level study, Emeritus Professor Edwards (Australian National University, Canberra) presents a balanced account of both the abstract theory and the applications of linear functional analysis. Written for readers with a basic knowledge of set theory, general topology, and vector spaces, the book includes an abundance of carefully chosen illustrative examples and excellent exercises at the end of each chapter. Beginning with a chapter of preliminaries on set theory and topology, Dr. Edwards then presents detailed, in-depth discussions of vector spaces and topological vector spaces, the Hahn-Banach theorem (including applications to potential theory, approximation theory, game theory, and other fields) and fixed-point theorems. Subsequent chapters focus on topological duals of certain spaces: radon measures, distribution and linear partial differential equations, open mapping and closed graph theorems, boundedness principles, duality theory, the theory of compact operators and the Krein-Milman theorem and its applications to commutative harmonic analysis. Clearly and concisely written, Dr. Edwards's book offers rewarding reading to mathematicians and physicists with an interest in the important field of functional analysis. Because of the broad scope of its coverage, this volume will be especially valuable to the reader with a basic knowledge of functional analysis who wishes to learn about parts of the subject other than his own specialties. A comprehensive 32-page bibliography supplies a rich source of references to the basic literature.

Applied Functional Analysis

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Author : Eberhard Zeidler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Applied Functional Analysis written by Eberhard Zeidler 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.

A theory is the more impressive, the simpler are its premises, the more distinct are the things it connects, and the broader is its range of applicability. Albert Einstein There are two different ways of teaching mathematics, namely, (i) the systematic way, and (ii) the application-oriented way. More precisely, by (i), I mean a systematic presentation of the material governed by the desire for mathematical perfection and completeness of the results. In contrast to (i), approach (ii) starts out from the question "What are the most important applications?" and then tries to answer this question as quickly as possible. Here, one walks directly on the main road and does not wander into all the nice and interesting side roads. The present book is based on the second approach. It is addressed to undergraduate and beginning graduate students of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems that are related to our real world and that have played an important role in the history of mathematics. The reader should sense that the theory is being developed, not simply for its own sake, but for the effective solution of concrete problems. viii Preface This introduction to functional analysis is divided into the following two parts: Part I: Applications to mathematical physics (the present AMS Vol. 108); Part II: Main principles and their applications (AMS Vol. 109).

Functional Analysis Spectral Theory And Applications

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Author : Manfred Einsiedler
language : en
Publisher: Springer
Release Date : 2017-11-21

Functional Analysis Spectral Theory And Applications written by Manfred Einsiedler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-21 with Mathematics categories.

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.

Introductory Functional Analysis With Applications

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Author : Erwin Kreyszig
language : en
Publisher: John Wiley & Sons
Release Date : 1991-01-16

Introductory Functional Analysis With Applications written by Erwin Kreyszig and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01-16 with Mathematics categories.

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

Convergence Structures And Applications To Functional Analysis

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Author : R. Beattie
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Convergence Structures And Applications To Functional Analysis written by R. Beattie 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 text offers a rigorous introduction into the theory and methods of convergence spaces and gives concrete applications to the problems of functional analysis. While there are a few books dealing with convergence spaces and a great many on functional analysis, there are none with this particular focus. The book demonstrates the applicability of convergence structures to functional analysis. Highlighted here is the role of continuous convergence, a convergence structure particularly appropriate to function spaces. It is shown to provide an excellent dual structure for both topological groups and topological vector spaces. Readers will find the text rich in examples. Of interest, as well, are the many filter and ultrafilter proofs which often provide a fresh perspective on a well-known result. Audience: This text will be of interest to researchers in functional analysis, analysis and topology as well as anyone already working with convergence spaces. It is appropriate for senior undergraduate or graduate level students with some background in analysis and topology.

Nonlinear Functional Analysis And Applications

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Author : Louis B. Rall
language : en
Publisher:
Release Date : 1971

Nonlinear Functional Analysis And Applications written by Louis B. Rall and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.

This volume contains the proceedings of an advanced seminar conducted by the Mathematics Research Center at the University of Wisconsin, Madison, held on October 12-14, 1970. This collection of papers is intended to give a reasonably self-contained introduction to the basic concepts and techniques of this field, highlighted by a few significant applications.

Nonlinear Functional Analysis And Its Applications

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Author : E. Zeidler
language : en
Publisher: Springer Science & Business Media
Release Date : 1989-12-11

Nonlinear Functional Analysis And Its Applications written by E. Zeidler 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 1989-12-11 with Mathematics categories.

This is the second of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics, and numerical analysis. The presentation is self -contained and accessible to the nonspecialist. Part II concerns the theory of monotone operators. It is divided into two subvolumes, II/A and II/B, which form a unit. The present Part II/A is devoted to linear monotone operators. It serves as an elementary introduction to the modern functional analytic treatment of variational problems, integral equations, and partial differential equations of elliptic, parabolic and hyperbolic type. This book also represents an introduction to numerical functional analysis with applications to the Ritz method along with the method of finite elements, the Galerkin methods, and the difference method. Many exercises complement the text. The theory of monotone operators is closely related to Hilbert's rigorous justification of the Dirichlet principle, and to the 19th and 20th problems of Hilbert which he formulated in his famous Paris lecture in 1900, and which strongly influenced the development of analysis in the twentieth century.

Functional Analysis And Control Theory

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Author : Stefan Rolewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 1987-10-31

Functional Analysis And Control Theory written by Stefan Rolewicz 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 1987-10-31 with Mathematics categories.

Approach your problems from the right It isn't that they can't see the solution. end and begin with the answers. Then, It is that they can't see the problem. one day, perhaps you will find the final G.K. Chesterton, The Scandal of Fa question. ther Brown 'The point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. Van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, cod ing theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical pro gramming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.

Computational Functional Analysis

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Author : Ramon E Moore
language : en
Publisher: Elsevier
Release Date : 2007-06-01

Computational Functional Analysis written by Ramon E Moore and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-01 with Technology & Engineering categories.

This course text fills a gap for first-year graduate-level students reading applied functional analysis or advanced engineering analysis and modern control theory. Containing 100 problem-exercises, answers, and tutorial hints, the first edition is often cited as a standard reference. Making a unique contribution to numerical analysis for operator equations, it introduces interval analysis into the mainstream of computational functional analysis, and discusses the elegant techniques for reproducing Kernel Hilbert spaces. There is discussion of a successful ''hybrid'' method for difficult real-life problems, with a balance between coverage of linear and non-linear operator equations. The authors successful teaching philosophy: ''We learn by doing'' is reflected throughout the book. - Contains 100 problem-exercises, answers and tutorial hints for students reading applied functional analysis - Introduces interval analysis into the mainstream of computational functional analysis