Spectral Theory for Linear Non-autonomous Differential Equations

This paper is concerned with linear equations x′ = A(t)x (t∈R, x∈Cn) having bounded growth and decay. Introducing a semigroup of linear operators Th, h≥0, by the formula (Thv)(t) = X(t, t − h)v(t − h), where v ∈ C0(Cn) consisting of Cn-valued bounded and continuous functions v on R satisfying lim v(t) = 0 as |t|→∞, X(t, s) is the evolutionary operator, one proves the spectral mapping theorem and the rotational invariance of σ(Th), and then discusses their applications