Описание: "The text is well written and easy to read. A great tool for any person interested in learning relations between functional analysis and model theory." -- MathSciNet During the last two decades, methods that originated within mathematical logic have exhibited powerful applications to Banach space theory, particularly set theory and model theory. This volume constitutes the first self-contained introduction to techniques of model theory in Banach space theory. The area of research has grown rapidly since this monograph's first appearance, but much of this material is still not readily available elsewhere. For instance, this volume offers a unified presentation of Krivine's theorem and the Krivine-Maurey theorem on stable Banach spaces, with emphasis on the connection between these results and basic model-theoretic notions such as types, indiscernible sequences, and ordinal ranks. Suitable for advanced undergraduates and graduate students of mathematics, this exposition does not presuppose expertise in either model theory or Banach space theory. Numerous exercises and historical notes supplement the text.
Описание: An introduction to the themes of mathematical analysis, this text is geared toward advanced undergraduate and graduate students. It assumes a familiarity with basic real analysis, metric space theory, linear algebra, and minimal knowledge of measures and Lebesgue integration, all of which are surveyed in the first chapter. Subsequent chapters explore the basic results of linear functional analysis: Stone-Weierstrass, Hahn-Banach, uniform boundedness and open mapping theorems, dual spaces, and basic properties of operators. Additional topics include function spaces, the Tychonov and Alaoglu theorems, Hilbert spaces, elementary Fourier analysis, and compact self-adjoint operators applied to Sturm-Liouville theory. "The author has a delightfully lively style which makes the book very readable," noted the Edinburgh Mathematical Society, "and there are numerous interesting and instructive problems."
Описание: "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."
Описание: Functional analysis provides a concise conceptual framework for linear control theory. This self-contained text, geared toward engineering students, demonstrates the subject''s unity. A wide range of powerful theorems illustrates inner product spaces; instability, controllability, and observability; minimum norm and time control; and distributed systems. 1980 edition.
Автор: Shilov, Georgi E. Название: Elementary Functional Analysis ISBN: 0486689239 ISBN-13(EAN): 9780486689234 Издательство: Dover Рейтинг: Цена: 2063 р. Наличие на складе: Поставка под заказ.
Описание: Introductory text covers basic structures of mathematical analysis (linear spaces, metric spaces, normed linear spaces, etc.), differential equations, orthogonal expansions, Fourier transforms including problems in the complex domain, especially involving the Laplace transform and more. Each chapter includes a set of problems, with hints and answers. Bibliography. 1974 edition."
Автор: Bachman, George Название: Functional Analysis ISBN: 0486402517 ISBN-13(EAN): 9780486402512 Издательство: Dover Рейтинг: Цена: 2868 р. Наличие на складе: Невозможна поставка.
Описание: Excellent treatment of the subject geared toward students with background in linear algebra, advanced calculus, physics and engineering. Text covers introduction to inner-product spaces, normed and metric spaces, and topological spaces; complete orthonormal sets, the Hahn-Banach theorem and its consequences, spectral notions, square roots, a spectral decomposition theorem, and many other related subjects. Chapters conclude with exercises intended to test and reinforce reader s understanding of text material. A glossary of definitions, detailed proofs of theorems, bibliography, and index of symbols round out this comprehensive text. 1966 edition."
Описание: This book by a prominent mathematician is appropriate for a single-semester course in applied numerical analysis for computer science majors and other upper-level undergraduate and graduate students. Although it does not cover actual programming, it focuses on the applied topics most pertinent to science and engineering professionals. An extensive range of topics includes round-off and function evaluation, real zeros of a function, simultaneous linear equations and matrices, interpolation and roundoff estimation, integration, and ordinary differential equations. Additional subjects include optimization, least squares, orthogonal functions, Fourier series, Chebyshev approximation, and random processes. The author stresses the teaching of mathematical concepts through visual aids, and numerous diagrams and illustrations complement the text.
Автор: Householder Alston S. Название: Principles of Numerical Analysis ISBN: 048645312X ISBN-13(EAN): 9780486453125 Издательство: Dover Рейтинг: Цена: 1948 р. Наличие на складе: Поставка под заказ.
Описание: This text explores aspects of matrix theory that are most useful in developing and appraising computational methods for solving systems of linear equations and for finding characteristic roots. Suitable for advanced undergraduates and graduate students, it assumes an understanding of the general principles of matrix algebra, including the Cayley-Hamilton theorem, characteristic roots and vectors, and linear dependence. An introductory chapter covers the Lanczos algorithm, orthogonal polynomials, and determinantal identities. Succeeding chapters examine norms, bounds, and convergence; localization theorems and other inequalities; and methods of solving systems of linear equations. The final chapters illustrate the mathematical principles underlying linear equations and their interrelationships. Topics include methods of successive approximation, direct methods of inversion, normalization and reduction of the matrix, and proper values and vectors. Each chapter concludes with a helpful set of references and problems.
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