# an introduction to the theory of linear spaces dover books on mathematics

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## An Introduction To The Theory Of Linear Spaces

**Author :**Georgi E. Shilov

**ISBN :**9780486139432

**Genre :**Mathematics

**File Size :**50. 15 MB

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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.

## Topological Vector Spaces And Distributions

**Author :**John Horvath

**ISBN :**9780486311036

**Genre :**Mathematics

**File Size :**42. 4 MB

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"The most readable introduction to the theory of vector spaces available in English and possibly any other language."—J. L. B. Cooper, MathSciNet Review Mathematically rigorous but user-friendly, this classic treatise discusses major modern contributions to the field of topological vector spaces. The self-contained treatment includes complete proofs for all necessary results from algebra and topology. Suitable for undergraduate mathematics majors with a background in advanced calculus, this volume will also assist professional mathematicians, physicists, and engineers. The precise exposition of the first three chapters—covering Banach spaces, locally convex spaces, and duality—provides an excellent summary of the modern theory of locally convex spaces. The fourth and final chapter develops the theory of distributions in relation to convolutions, tensor products, and Fourier transforms. Augmented with many examples and exercises, the text includes an extensive bibliography.

## Introduction To Spectral Theory In Hilbert Space

**Author :**Gilbert Helmberg

**ISBN :**9781483164175

**Genre :**Mathematics

**File Size :**44. 21 MB

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North-Holland Series in Applied Mathematics and Mechanics, Volume 6: Introduction to Spectral Theory in Hilbert Space focuses on the mechanics, principles, and approaches involved in spectral theory in Hilbert space. The publication first elaborates on the concept and specific geometry of Hilbert space and bounded linear operators. Discussions focus on projection and adjoint operators, bilinear forms, bounded linear mappings, isomorphisms, orthogonal subspaces, base, subspaces, finite dimensional Euclidean space, and normed linear spaces. The text then takes a look at the general theory of linear operators and spectral analysis of compact linear operators, including spectral decomposition of a compact selfadjoint operator, weakly convergent sequences, spectrum of a compact linear operator, and eigenvalues of a linear operator. The manuscript ponders on the spectral analysis of bounded linear operators and unbounded selfadjoint operators. Topics include spectral decomposition of an unbounded selfadjoint operator and bounded normal operator, functions of a unitary operator, step functions of a bounded selfadjoint operator, polynomials in a bounded operator, and order relation for bounded selfadjoint operators. The publication is a valuable source of data for mathematicians and researchers interested in spectral theory in Hilbert space.

## Linear Algebra

**Author :**Georgi? Evgen?evich Shilov

**ISBN :**048663518X

**Genre :**Mathematics

**File Size :**34. 68 MB

**Format :**PDF

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Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.

## The Theory Of Linear Viscoelasticity

**Author :**D. R. Bland

**ISBN :**9780486816388

**Genre :**Technology & Engineering

**File Size :**85. 18 MB

**Format :**PDF

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This concise introduction to the concepts of viscoelasticity focuses on stress analysis. Three detailed individual sections present examples of stress-related problems. In addition, it explains procedures for model fitting to measured values of complex modulus or compliance. The text begins with an introduction to the concepts of viscoelasticity. Succeeding chapters explore the foundations of three-dimensional linear viscoelasticity and stress analysis. Sinusoidal oscillation problems, quasi-static problems, and dynamic problems receive particular attention. The final chapter examines model fitting to measured values of complex modulus or compliance. Numerous examples and figures illuminate the text.

## Logic The Theory Of Formal Inference

**Author :**Alice Ambrose

**ISBN :**9780486796772

**Genre :**Mathematics

**File Size :**47. 32 MB

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Geared toward college undergraduates new to the subject, this concise introduction features a preliminary section on truth-functions. Two additional parts on quantification and classes, each subdivided into numerous brief specifics, complete the overview. 1961 edition.

## Unbounded Linear Operators

**Author :**Seymour Goldberg

**ISBN :**9780486453316

**Genre :**Mathematics

**File Size :**74. 28 MB

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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.