We discuss the spectral properties of higher order ordinary differential operators. If the coefficients differ from constants by small perturbations, then the spectral properties are preserved. In this context, “small perturbations” 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 with the help of uniform asymptotic integration techniques. Copyright 2001 Academic Press.
Document Type: Research Article
Fachbereich Mathematik/Informatik, Universität Osnabrück, Osnabrück, Germany 2:
Department of Mathematics, University of Tennessee, Knoxville, Tennessee, 37996