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 ${\mathbf{L}}_p(\mathbb{R})(1\le p<\infty )$. As an application of general results, new spectral properties of the perturbed Hill operator are derived.