Functional Differential Operators and Equations

by U.G. Kurbatov

Overview

This book deals with linear functional differential equations and operator theory methods for their investigation.
The main topics are: the equivalence of the input-output stability of the equation Lx = f and the invertibility of the operator L in the class of casual operators; the equivalence of input-output and exponential stability; the equivalence of the dichotomy of solutions for the homogeneous equation Lx = 0 and the invertibility of the operator L; the properties of Green's function; the independence of the stability of an equation from the norm on the space of solutions; shift invariant functional differential equations in Banach space; the possibility of the reduction of an equation of neutral type to an equation of retarded type; special full subalgebras of integral and difference operators, and operators with unbounded memory; and the analogue of Fredholm's alternative for operators with almost periodic coefficients where one-sided invertibility implies two-sided invertibility.
Audience: This monograph will be of interest to students and researchers working in functional differential equations and operator theory and is recommended for graduate level courses.

Product Details

ISBN-13:	9789048151837
Publisher:	Springer Netherlands
Publication date:	01/11/2011
Series:	Mathematics and Its Applications , #473
Edition description:	Softcover reprint of hardcover 1st ed. 1999
Pages:	434
Product dimensions:	6.30(w) x 9.45(h) x 0.36(d)

Table of Contents

Preface. I. Functional Analysis Preliminaries. II. The Initial Value Problem. III. Stability. IV. Shift invariant operators and equations. V. Operators with varying coefficients. VI. Differential difference equations. Comments. Bibliography. Index. Notation Index.

Editorial Reviews

U.G. Kurbatov

Functional Differential Operators and Equations

"This book provides a thorough and rigorous presentation of the use of operator theory methods to study the linear theory of functional-differential equations . . . It is a practically self-contained book by means of which students and researchers working in functional analysis can be introduced to the abstract linear theory of functional-differential equations."—MATHEMATICAL REVIEWS

From the Publisher