Non-resonance for linear differential systems

Abstract

SynopsisThe existence of a set of real numbers σ, depending only on ∧0, is established such that if λ ∉ σ, the system Y'=(i∧0 + R)Y can be transformed into a system Z' = (i∧ + S)Z of the Levinson form. Here ∧0 and ∧ are real diagonal matrices, with ∧0 constant, and R(x) = ξ(x)T(λx). The scalar factor ξ(x) is o(l) (x →∞) and T belongs to a certain class of periodic matrices. The consequences for non-resonance, and the necessity of this class, are discussed.