Uniform Asymptoti Integration of a Family of Linear Differential Systems

Abstract

Consider a family of linear differential systems y′ =A(x, z)y depending on a parameter z Assume, as in Levinson's Theorem, that A = Λ + R with Λ diagonal and R integrable. We discuss the problem of asymptotically solving this systemwith uniform (in z) control on the error terms.Questions of this type occur in the spectral theory of differential operators.