The spectrum of differential operators of order 2n with almost constant coefficients

We discuss the spectral properties of higher order ordinary differential op erators. If the coefficients differ from constants by small perturbations, then the spectral properties are preserved. In this context, "small perturb ations" are either short range (i.e., integrable) or long range, but slowly varying. This generalizes classical results on second order operators. Our approach relies on an analysis of the associated differential equations wi th the help of uniform asymptotic integration techniques. (C) 2001 Academic Press.