<p>This book deals with linear functional differential equations and operator theory methods for their investigation. <br> The main topics are: the equivalence of the input-output stability of the equation Lx = &amp;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. <br> 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.</p>

Functional Differential Operators and Equations (Mathematics and Its Applications, 473)

Science & Math

Kurbatov, U.G.

Mathematics

Kluwer

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.

Springer

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Books by Kurbatov, U.G.

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Functional Differential Operators and Equations (Mathematics and Its Applications, 473)

Functional Differential Operators and Equations (Mathematics and Its Applications, 473)