Abstract
The linear autonomous, neutral system of functional differential equations d dt (μ ∗ x(t) + ƒ(t)) = v ∗ s(t) + g(t) (t ⩾ o) , (∗) x( t) = ϑ( t) ( t ⩽ 0), in a fading memory space is studied. Here μ and ν are matrix-valued measures supported on [0, ∞), finite with respect to a weight function, and ƒ, g, and ϑ are C n -valued, continuous or locaily integrable functions, bounded with respect to a fading memory norm. Conditions which imply that solutions of (∗) can be decomposed into a stable part and an unstable part are given. These conditions are of frequency domain type. The usual assumption that the singular part of μ vanishes is not needed. The results can be used to decompose the semigroup generated by (∗) into a stable part and an unstable part.
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