Elementary Functional Analysis
Georgi E. Shilov
avr. 2013 · Courier Corporation
3,5star
4 avisreport
E-book
352
Pages
reportLes notes et avis ne sont pas vérifiés. En savoir plus
À propos de cet e-book
In this introductory work on mathematical analysis, the noted mathematician Georgi E. Shilov begins with an extensive and important chapter on the basic structures of mathematical analysis: linear spaces, metric spaces, normed linear spaces, Hilbert spaces, and normed algebras. The standard models for all these spaces are sets of functions (hence the term "functional analysis"), rather than sets of points in a finite-dimensional space.
Chapter 2 is devoted to differential equations, and contains the basic theorems on existence and uniqueness of solutions of ordinary differential equations for functions taking values in a Banach space. The solution of the linear equation with constant (operator) coefficients is written in general form in terms of the exponential of the operator. This leads, in the finite-dimensional case, to explicit formulas not only for the solutions of first-order equations, but also to the solutions of higher-order equations and systems of equations. The third chapter presents a theory of curvature for curve in a multidimensional space.
The final two chapters essentially comprise an introduction to Fourier analysis. In the treatment of orthogonal expansions, a key role is played by Fourier series and the various kinds of convergence and summability for such series. The material on Fourier transforms, in addition to presenting the more familiar theory, also deals with problems in the complex domain, in particular with problems involving the Laplace transform.
Designed for students at the upper-undergraduate or graduate level, the text includes a set of problems for each chapter, with hints and answers at the end of the book.
Chapter 2 is devoted to differential equations, and contains the basic theorems on existence and uniqueness of solutions of ordinary differential equations for functions taking values in a Banach space. The solution of the linear equation with constant (operator) coefficients is written in general form in terms of the exponential of the operator. This leads, in the finite-dimensional case, to explicit formulas not only for the solutions of first-order equations, but also to the solutions of higher-order equations and systems of equations. The third chapter presents a theory of curvature for curve in a multidimensional space.
The final two chapters essentially comprise an introduction to Fourier analysis. In the treatment of orthogonal expansions, a key role is played by Fourier series and the various kinds of convergence and summability for such series. The material on Fourier transforms, in addition to presenting the more familiar theory, also deals with problems in the complex domain, in particular with problems involving the Laplace transform.
Designed for students at the upper-undergraduate or graduate level, the text includes a set of problems for each chapter, with hints and answers at the end of the book.
Notes et avis
3,5
4 avis
À propos de l'auteur
Soviet mathematician Georgi E. Shilov (1917-75) was a longtime Professor of Mathematics at Moscow State University and the author of several other successful Dover reprints.
Donner une note à cet e-book
Dites-nous ce que vous en pensez.
Informations sur la lecture
Smartphones et tablettes
Installez l'application Google Play Livres pour Android et iPad ou iPhone. Elle se synchronise automatiquement avec votre compte et vous permet de lire des livres en ligne ou hors connexion, où que vous soyez.
Ordinateurs portables et de bureau
Vous pouvez écouter les livres audio achetés sur Google Play à l'aide du navigateur Web de votre ordinateur.
Liseuses et autres appareils
Pour lire sur des appareils e-Ink, comme les liseuses Kobo, vous devez télécharger un fichier et le transférer sur l'appareil en question. Suivez les instructions détaillées du Centre d'aide pour transférer les fichiers sur les liseuses compatibles.
