Banach Spaces Of Analytic Functions

Author: Kenneth Hoffman
Publisher: Courier Corporation
ISBN: 048614996X
Size: 49.97 MB
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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

Author: S. Banach
Publisher: Elsevier
ISBN: 9780080887203
Size: 14.27 MB
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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

Author: Martin Davis
Publisher: Courier Corporation
ISBN: 0486499839
Size: 30.31 MB
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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

Author: Marian Fabian
Publisher: Springer Science & Business Media
ISBN: 1475734808
Size: 41.27 MB
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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

Author: Avner Friedman
Publisher: Courier Corporation
ISBN: 9780486152912
Size: 19.33 MB
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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.

Differential Calculus On Normed Spaces

Author: Henri Cartan
Publisher: Createspace Independent Publishing Platform
ISBN: 9781548749323
Size: 35.74 MB
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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.

Theory Of Hp Spaces

Author: Peter L. Duren
Publisher: Courier Corporation
ISBN: 9780486411842
Size: 11.70 MB
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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

Author: Magnús M. Halldórsson
Publisher: Springer
ISBN: 366247672X
Size: 38.55 MB
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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.

Analysis In Euclidean Space

Author: Kenneth Hoffman
Publisher: Courier Corporation
ISBN: 0486135845
Size: 76.71 MB
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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.

Square Summable Power Series

Author: Louis de Branges
Publisher: Courier Corporation
ISBN: 0486789993
Size: 66.88 MB
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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.