Absence of eigenvalues for integro-differential operators with periodic coefficients

Abstract

Applying perturbation theory methods, the absence of the point spectrum for some nonselfadjoint integro-differential operators is investigated. The considered differential operators are of arbitrary order and act in either $\mathbf{L}_{p}(\mathbb{R}_{+})$ or $\mathbf{L}_{p}(\mathbb{R}) (1\leq p<\infty)$. As an application of general results, new spectral properties of the perturbed Hill operator are derived.