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 = &mathsf; 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.
| ISBN: | 9789048151837 |
| Publication date: | 28th March 2011 |
| Author: | V G Kurbatov |
| Publisher: | Springer an imprint of Springer Netherlands |
| Format: | Paperback |
| Pagination: | 454 pages |
| Series: | Mathematics and Its Applications |
| Genres: |
Differential calculus and equations Integral calculus and equations Complex analysis, complex variables Functional analysis and transforms |
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 = &mathsf; 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.
Functional Differential Operators and Equations features in the following genres: Differential calculus and equations, Integral calculus and equations, Complex analysis, complex variables, Functional analysis and transforms
Paperback. Not Available.
Functional Differential Operators and Equations was written by V G Kurbatov and published by Springer an imprint of Springer Netherlands
Functional Differential Operators and Equations has 454 pages
Yes it is part of Mathematics and Its Applications series