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Banach Spaces of Analytic Functions

Banach Spaces of Analytic Functions Author Kenneth Hoffman
ISBN-10 9780486149967
Release 2014-06-10
Pages 224
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This rigorous investigation of Hardy spaces and the invariant subspace problem is suitable for advanced undergraduates and graduates, covering complex functions, harmonic analysis, and functional analysis. 1962 edition.

Theory of Linear Operations

Theory of Linear Operations Author S. Banach
ISBN-10 0080887201
Release 1987-03-01
Pages 248
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This classic work by the late Stefan Banach has been translated into English so as to reach a yet wider audience. It contains the basics of the algebra of operators, concentrating on the study of linear operators, which corresponds to that of the linear forms a1x1 + a2x2 + ... + anxn of algebra. The book gathers results concerning linear operators defined in general spaces of a certain kind, principally in Banach spaces, examples of which are: the space of continuous functions, that of the pth-power-summable functions, Hilbert space, etc. The general theorems are interpreted in various mathematical areas, such as group theory, differential equations, integral equations, equations with infinitely many unknowns, functions of a real variable, summation methods and orthogonal series. A new fifty-page section (``Some Aspects of the Present Theory of Banach Spaces'') complements this important monograph.

A First Course in Functional Analysis

A First Course in Functional Analysis Author Martin Davis
ISBN-10 9780486499833
Release 2013
Pages 110
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Designed for undergraduate mathematics majors, this introductory treatment is based on the distinguished author's lecture notes. The self-contained exposition of Gelfand's proof of Wiener's theorem explores set theoretic preliminaries, normed linear spaces and algebras, functions on Banach spaces, homomorphisms on normed linear spaces, and analytic functions into a Banach space. 1966 edition.

Functional Analysis and Infinite Dimensional Geometry

Functional Analysis and Infinite Dimensional Geometry Author Marian Fabian
ISBN-10 9781475734805
Release 2013-04-17
Pages 451
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This book introduces the basic principles of functional analysis and areas of Banach space theory that are close to nonlinear analysis and topology. The text can be used in graduate courses or for independent study. It includes a large number of exercises of different levels of difficulty, accompanied by hints.

Generalized Functions and Partial Differential Equations

Generalized Functions and Partial Differential Equations Author Avner Friedman
ISBN-10 048615291X
Release 2011-11-30
Pages 352
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This self-contained text details developments in the theory of generalized functions and the theory of distributions, and it systematically applies them to a variety of problems in partial differential equations. 1963 edition.

Introduction to Banach Algebras Operators and Harmonic Analysis

Introduction to Banach Algebras  Operators  and Harmonic Analysis Author H. Garth Dales
ISBN-10 0521535840
Release 2003-11-13
Pages 324
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Introduction to important topics in functional analysis from leading researchers. Ideal for graduate students.

Invariant Subspaces

Invariant Subspaces Author Heydar Radjavi
ISBN-10 9780486153025
Release 2011-11-30
Pages 256
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Broad survey focuses on operators on separable Hilbert spaces. Topics include normal operators, analytic functions of operators, shift operators, invariant subspace lattices, compact operators, invariant and hyperinvariant subspaces, more. 1973 edition.

Differential Calculus on Normed Spaces

Differential Calculus on Normed Spaces Author Henri Cartan
ISBN-10 154874932X
Release 2017-08-02
Pages 176
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This classic and long out of print text by the famous French mathematician Henri Cartan, has finally been retitled and reissued as an unabridged reprint of the Kershaw Publishing Company 1971 edition at remarkably low price for a new generation of university students and teachers. It provides a concise and beautifully written course on rigorous analysis. Unlike most similar texts, which usually develop the theory in either metric or Euclidean spaces, Cartan's text is set entirely in normed vector spaces, particularly Banach spaces. This not only allows the author to develop carefully the concepts of calculus in a setting of maximal generality, it allows him to unify both single and multivariable calculus over either the real or complex scalar fields by considering derivatives of nth orders as linear transformations. This prepares the student for the subsequent study of differentiable manifolds modeled on Banach spaces as well as graduate analysis courses, where normed spaces and their isomorphisms play a central role. More importantly, it's republication in an inexpensive edition finally makes available again the English translations of both long separated halves of Cartan's famous 1965-6 analysis course at the University of Paris: The second half has been in print for over a decade as Differential Forms , published by Dover Books. Without the first half, it has been very difficult for readers of that second half text to be prepared with the proper prerequisites as Cartan originally intended. With both texts now available at very affordable prices, the entire course can now be easily obtained and studied as it was originally intended. The book is divided into two chapters. The first develops the abstract differential calculus. After an introductory section providing the necessary background on the elements of Banach spaces, the Frechet derivative is defined, and proofs are given of the two basic theorems of differential calculus: The mean value theorem and the inverse function theorem. The chapter proceeds with the introduction and study of higher order derivatives and a proof of Taylor's formula. It closes with a study of local maxima and minima including both necessary and sufficient conditions for the existence of such minima. The second chapter is devoted to differential equations. Then the general existence and uniqueness theorems for ordinary differential equations on Banach spaces are proved. Applications of this material to linear equations and to obtaining various properties of solutions of differential equations are then given. Finally the relation between partial differential equations of the first order and ordinary differential equations is discussed. The prerequisites are rigorous first courses in calculus on the real line (elementary analysis), linear algebra on abstract vectors spaces with linear transformations and the basic definitions of topology (metric spaces, topology,etc.) A basic course in differential equations is advised as well. Together with its' sequel, Differential Calculus On Normed Spaces forms the basis for an outstanding advanced undergraduate/first year graduate analysis course in the Bourbakian French tradition of Jean Dieudonn�'s Foundations of Modern Analysis, but a more accessible level and much more affordable then that classic.

Square Summable Power Series

Square Summable Power Series Author Louis de Branges
ISBN-10 9780486789996
Release 2015-02-18
Pages 112
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Text for advanced undergraduate and graduate students introduces Hilbert space and analytic function theory. Its principal feature is the extensive use of formal power series methods to obtain and sometimes reformulate results of analytic function theory. 1966 edition.

Analysis in Euclidean Space

Analysis in Euclidean Space Author Kenneth Hoffman
ISBN-10 9780486135847
Release 2013-01-16
Pages 448
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Developed for a beginning course in mathematical analysis, this text focuses on concepts, principles, and methods, offering introductions to real and complex analysis and complex function theory. 1975 edition.

Theory of Hp Spaces

Theory of Hp Spaces Author Peter L. Duren
ISBN-10 0486411842
Release 2000
Pages 292
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A blend of classical and modern techniques and viewpoints, this text examines harmonic and subharmonic functions, the basic structure of Hp functions, applications, Taylor coefficients, interpolation theory, more. 1970 edition.

Automata Languages and Programming

Automata  Languages  and Programming Author Magnús M. Halldórsson
ISBN-10 9783662476727
Release 2015-06-19
Pages 1111
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The two-volume set LNCS 9134 and LNCS 9135 constitutes the refereed proceedings of the 42nd International Colloquium on Automata, Languages and Programming, ICALP 2015, held in Kyoto, Japan, in July 2015. The 143 revised full papers presented were carefully reviewed and selected from 507 submissions. The papers are organized in the following three tracks: algorithms, complexity, and games; logic, semantics, automata, and theory of programming; and foundations of networked computation: models, algorithms, and information management.

Infinite Dimensional Analysis

Infinite Dimensional Analysis Author Charalambos D. Aliprantis
ISBN-10 9783662039618
Release 2013-03-14
Pages 673
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This book presents functional analytic methods in a unified manner with applications to economics, social sciences, and engineering. Ideal for those without an extensive background in the area, it develops topology, convexity, Banach lattices, integration, correspondences, and the analytic approach to Markov processes. Many of the results were previously available only in esoteric monographs and will interest researchers and students who will find the material readily applicable to problems in control theory and economics.

An Advanced Complex Analysis Problem Book

An Advanced Complex Analysis Problem Book Author Daniel Alpay
ISBN-10 9783319160597
Release 2015-11-13
Pages 521
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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.

The Cauchy Transform

The Cauchy Transform Author Joseph A. Cima
ISBN-10 9780821838716
Release 2006
Pages 272
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The Cauchy transform of a measure on the circle is a subject of both classical and current interest with a sizable literature. This book is a thorough, well-documented, and readable survey of this literature and includes full proofs of the main results of the subject. This book also covers more recent perturbation theory as covered by Clark, Poltoratski, and Aleksandrov and contains an in-depth treatment of Clark measures.

Theory of Approximation of Functions of a Real Variable

Theory of Approximation of Functions of a Real Variable Author A. F. Timan
ISBN-10 9781483184814
Release 2014-07-22
Pages 644
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Theory of Approximation of Functions of a Real Variable discusses a number of fundamental parts of the modern theory of approximation of functions of a real variable. The material is grouped around the problem of the connection between the best approximation of functions to their structural properties. This text is composed of eight chapters that highlight the relationship between the various structural properties of real functions and the character of possible approximations to them by polynomials and other functions of simple construction. Each chapter concludes with a section containing various problems and theorems, which supplement the main text. The first chapters tackle the Weierstrass's theorem, the best approximation by polynomials on a finite segment, and some compact classes of functions and their structural properties. The subsequent chapters describe some properties of algebraic polynomials and transcendental integral functions of exponential type, as well as the direct theorems of the constructive theory of functions. These topics are followed by discussions of differential and constructive characteristics of converse theorems. The final chapters explore other theorems connecting the best approximations functions with their structural properties. These chapters also deal with the linear processes of approximation of functions by polynomials. The book is intended for post-graduate students and for mathematical students taking advanced courses, as well as to workers in the field of the theory of functions.

Elementary Functional Analysis

Elementary Functional Analysis Author Barbara MacCluer
ISBN-10 9780387855295
Release 2008-10-20
Pages 208
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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.