Theory of Linear Operations

Author: Stefan Banach,F. Jellett

Publisher: N.A

ISBN: 9780486469836

Category: Mathematics

Page: 237

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Written by the founder of functional analysis, this is the first text on linear operator theory. Additional topics include the calculus of variations and theory of integral equations. 1987 edition.

Theory of Linear Operators in Hilbert Space

Author: Naum Il?ich Akhiezer,Izrail? Markovich Glazman

Publisher: Courier Corporation

ISBN: 0486677486

Category: Mathematics

Page: 218

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This classic textbook introduces linear operators in Hilbert Space, and presents the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. Invaluable for every mathematician and physicist. 1961, 1963 edition.

Theory of Linear Operators in Hilbert Space

Author: N. I. Akhiezer,I. M. Glazman

Publisher: Courier Corporation

ISBN: 0486318656

Category: Mathematics

Page: 378

View: 1916

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This classic textbook by two mathematicians from the USSR's prestigious Kharkov Mathematics Institute introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. It is directed to students at graduate and advanced undergraduate levels, but because of the exceptional clarity of its theoretical presentation and the inclusion of results obtained by Soviet mathematicians, it should prove invaluable for every mathematician and physicist. 1961, 1963 edition.

Lectures on Linear Algebra

Author: I. M. Gelfand

Publisher: Courier Corporation

ISBN: 9780486660820

Category: Mathematics

Page: 185

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Prominent Russian mathematician's concise, well-written exposition considers n-dimensional spaces, linear and bilinear forms, linear transformations, canonical form of an arbitrary linear transformation, and an introduction to tensors. While not designed as an introductory text, the book's well-chosen topics, brevity of presentation, and the author's reputation will recommend it to all students, teachers, and mathematicians working in this sector.

Elements of the Theory of Functions and Functional Analysis

Author: Andre? Nikolaevich Kolmogorov,Serge? Vasil?evich Fomin,S. V. Fomin

Publisher: Courier Corporation

ISBN: 9780486406831

Category: Mathematics

Page: 288

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Advanced-level text, now available in a single volume, discusses metric and normed spaces, continuous curves in metric spaces, measure theory, Lebesque intervals, Hilbert space, more. Exercises. 1957 edition.

Mathematical Logic

Author: Stephen Cole Kleene

Publisher: Courier Corporation

ISBN: 0486317072

Category: Mathematics

Page: 416

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Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.

Introduction to Hilbert Space and the Theory of Spectral Multiplicity

Second Edition

Author: Paul R. Halmos

Publisher: Courier Dover Publications

ISBN: 048682683X

Category: Mathematics

Page: 128

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Concise introductory treatment consists of three chapters: The Geometry of Hilbert Space, The Algebra of Operators, and The Analysis of Spectral Measures. A background in measure theory is the sole prerequisite. 1957 edition.

An Introduction to Lebesgue Integration and Fourier Series

Author: Howard J. Wilcox,David L. Myers

Publisher: Courier Corporation

ISBN: 9780486682938

Category: Mathematics

Page: 159

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This book arose out of the authors' desire to present Lebesgue integration and Fourier series on an undergraduate level, since most undergraduate texts do not cover this material or do so in a cursory way. The result is a clear, concise, well-organized introduction to such topics as the Riemann integral, measurable sets, properties of measurable sets, measurable functions, the Lebesgue integral, convergence and the Lebesgue integral, pointwise convergence of Fourier series and other subjects. The authors not only cover these topics in a useful and thorough way, they have taken pains to motivate the student by keeping the goals of the theory always in sight, justifying each step of the development in terms of those goals. In addition, whenever possible, new concepts are related to concepts already in the student's repertoire. Finally, to enable readers to test their grasp of the material, the text is supplemented by numerous examples and exercises. Mathematics students as well as students of engineering and science will find here a superb treatment, carefully thought out and well presented , that is ideal for a one semester course. The only prerequisite is a basic knowledge of advanced calculus, including the notions of compactness, continuity, uniform convergence and Riemann integration.

An Introduction to the Theory of Linear Spaces

Author: Georgi E. Shilov,Richard A. Silverman

Publisher: Courier Corporation

ISBN: 0486139433

Category: Mathematics

Page: 320

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Introductory treatment offers a clear exposition of algebra, geometry, and analysis as parts of an integrated whole rather than separate subjects. Numerous examples illustrate many different fields, and problems include hints or answers. 1961 edition.

Matrices and Linear Transformations

Second Edition

Author: Charles G. Cullen

Publisher: Courier Corporation

ISBN: 0486132412

Category: Mathematics

Page: 336

View: 421

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Undergraduate-level introduction to linear algebra and matrix theory. Explores matrices and linear systems, vector spaces, determinants, spectral decomposition, Jordan canonical form, much more. Over 375 problems. Selected answers. 1972 edition.

Aufbaukurs Funktionalanalysis und Operatortheorie

Distributionen - lokalkonvexe Methoden - Spektraltheorie

Author: Winfried Kaballo

Publisher: Springer-Verlag

ISBN: 3642377947

Category: Mathematics

Page: 493

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In diesem Buch finden Sie eine Einführung in die Funktionalanalysis und Operatortheorie auf dem Niveau eines Master-Studiengangs. Ausgehend von Fragen zu partiellen Differenzialgleichungen und Integralgleichungen untersuchen Sie lineare Gleichungen im Hinblick auf Existenz und Struktur von Lösungen sowie deren Abhängigkeit von Parametern. Dazu lernen Sie verschiedene Konzepte und Methoden kennen: Distributionen, Fourier-Transformation, Sobolev-Räume, Dualitätstheorie im Rahmen lokalkonvexer Räume, topologische Tensorprodukte, exakte Sequenzen, Banachalgebren, Fredholmoperatoren, Funktionalkalküle sowie selbstadjungierte Operatoren und ihre Rolle in der Quantenmechanik. Das Buch ist ausführlich und leicht verständlich geschrieben, die Konzepte und Resultate werden durch Abbildungen und viele Beispiele illustriert. Anhand zahlreicher Übungsaufgaben (mit Lösungen auf der Website zum Buch) können Sie Ihr Verständnis des Stoffes testen, anhand anderer diesen selbstständig weiterentwickeln.

Semigroups of Linear Operators and Applications

Second Edition

Author: Jerome A. Goldstein

Publisher: Courier Dover Publications

ISBN: 048681257X

Category: Mathematics

Page: 320

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Advanced graduate-level treatment of semigroup theory explores semigroups of linear operators and linear Cauchy problems. The text features challenging exercises and emphasizes motivation, heuristics, and further applications. 1985 edition.

Mathematics for Quantum Mechanics

An Introductory Survey of Operators, Eigenvalues, and Linear Vector Spaces

Author: John David Jackson

Publisher: Courier Corporation

ISBN: 048613881X

Category: Science

Page: 112

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This concise text for advanced undergraduates and graduate students covers eigenvalue problems, orthogonal functions and expansions, the Sturm-Liouville theory and linear operators on functions, and linear vector spaces. 1962 edition.

Lineare Operatoren in Hilberträumen

Teil 1 Grundlagen

Author: Joachim Weidmann

Publisher: Springer-Verlag

ISBN: 9783322800947

Category: Mathematics

Page: 475

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Behandelt werden die Grundlagen der Theorie zum Thema Lineare Operatoren in Hilberträumen, wie sie üblicherweise in Standardvorlesungen für Mathematiker und Physiker vorgestellt werden.

Lineare Operatoren in Hilberträumen

Teil II: Anwendungen

Author: Joachim Weidmann

Publisher: Springer-Verlag

ISBN: 3322800954

Category: Mathematics

Page: 404

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Die im ersten Teil des Buchs dargestellten Grundlagen der Theorie der linearen Operatoren in Hilberträumen werden hier benutzt, um die Spektraltheorie von Ein- und Mehrteilchen-Schrödingeroperatoren sowie des Dirac-Operators eingehend zu untersuchen.

Foundations of Modern Analysis

Author: Avner Friedman

Publisher: Courier Corporation

ISBN: 9780486640624

Category: Mathematics

Page: 250

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Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Only book of its kind. Unusual topics, detailed analyses. Problems. Excellent for first-year graduate students, almost any course on modern analysis. Preface. Bibliography. Index.

Unbounded Linear Operators

Theory and Applications

Author: Seymour Goldberg

Publisher: Courier Corporation

ISBN: 0486453316

Category: Mathematics

Page: 199

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This volume presents a systematic treatment of the theory of unbounded linear operators in normed linear spaces with applications to differential equations. Largely self-contained, it is suitable for advanced undergraduates and graduate students, and it only requires a familiarity with metric spaces and real variable theory. After introducing the elementary theory of normed linear spaces--particularly Hilbert space, which is used throughout the book--the author develops the basic theory of unbounded linear operators with normed linear spaces assumed complete, employing operators assumed closed only when needed. Other topics include strictly singular operators; operators with closed range; perturbation theory, including some of the main theorems that are later applied to ordinary differential operators; and the Dirichlet operator, in which the author outlines the interplay between functional analysis and "hard" classical analysis in the study of elliptic partial differential equations. In addition to its readable style, this book's appeal includes numerous examples and motivations for certain definitions and proofs. Moreover, it employs simple notation, eliminating the need to refer to a list of symbols.


Functional Analysis

Theory and Applications

Author: R.E. Edwards

Publisher: Courier Corporation

ISBN: 0486145107

Category: Mathematics

Page: 800

View: 3539

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Massive compilation offers detailed, in-depth discussions of vector spaces, Hahn-Banach theorem, fixed-point theorems, duality theory, Krein-Milman theorem, theory of compact operators, much more. Many examples and exercises. 32-page bibliography. 1965 edition.

Introduction to Spectral Theory in Hilbert Space

Author: Gilbert Helmberg

Publisher: Courier Dover Publications

ISBN: 0486466221

Category: Mathematics

Page: 346

View: 1130

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This text introduces students to Hilbert space and bounded self-adjoint operators, as well as the spectrum of an operator and its spectral decomposition. The author, Emeritus Professor of Mathematics at the University of Innsbruck, Austria, has ensured that the treatment is accessible to readers with no further background than a familiarity with analysis and analytic geometry. Starting with a definition of Hilbert space and its geometry, the text explores the general theory of bounded linear operators, the spectral analysis of compact linear operators, and unbounded self-adjoint operators. Extensive appendixes offer supplemental information on the graph of a linear operator and the Riemann-Stieltjes and Lebesgue integration.