Elementary Functional Analysis

Nonfiction, Science & Nature, Mathematics, Functional Analysis
Cover of the book Elementary Functional Analysis by Georgi E. Shilov, Dover Publications
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Georgi E. Shilov ISBN: 9780486318684
Publisher: Dover Publications Publication: April 15, 2013
Imprint: Dover Publications Language: English
Author: Georgi E. Shilov
ISBN: 9780486318684
Publisher: Dover Publications
Publication: April 15, 2013
Imprint: Dover Publications
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Dover Publications

Cover of the book An Introduction to the Theory of Canonical Matrices by Georgi E. Shilov
Cover of the book Craftsman Bungalows by Georgi E. Shilov
Cover of the book Othello Thrift Study Edition by Georgi E. Shilov
Cover of the book Elements of Chemistry by Georgi E. Shilov
Cover of the book The Fourth Dimension Simply Explained by Georgi E. Shilov
Cover of the book Foundations of Laser Spectroscopy by Georgi E. Shilov
Cover of the book Denslow's Mother Goose by Georgi E. Shilov
Cover of the book Complete Guide to Home Canning and Preserving (Second Revised Edition) by Georgi E. Shilov
Cover of the book American Drawings and Prints by Georgi E. Shilov
Cover of the book The Adventures of Old Mr. Toad by Georgi E. Shilov
Cover of the book Fantastic Beasts of the Nineteenth Century by Georgi E. Shilov
Cover of the book Mathematical Games, Abstract Games by Georgi E. Shilov
Cover of the book Needle-Made Laces and Net Embroideries by Georgi E. Shilov
Cover of the book The Interpretation of Dreams by Georgi E. Shilov
Cover of the book Everyday Fashions of the Forties As Pictured in Sears Catalogs by Georgi E. Shilov
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy