Necessary and sufficient conditions for invertibility of uniformly c- continuous functional-differential operators (Q914939)

This article deals with the convertibility property for the so-called uniformly c-continuous operators \(A\in L(C^ m,C^ 0)\) where \(C^ k\) is a space of bounded and continuous together with derivatives of order 1,...,k functions x: \({\mathbb{R}}\to {\mathbb{R}}^ n\). Necessary and sufficient conditions of convertibility of these operators are formulated in terms of existence of approximating sequences of operators with some special properties. These results are generalizations and analogues of the classical Favard theorem on the convertibility of linear differential equations with almost periodic coefficients.