On half‐line spectra for a class of non‐self‐adjoint Hill operators

Abstract

AbstractIn 1980, Gasymov showed that non‐self‐adjoint Hill operators with complex‐valued periodic potentials of the type $ V(x) = \sum ^{\infty} _{k=1} a_{k} e^{ikx} $, with $ \sum ^{\infty} _{k=1} \vert a_{k} \vert < \infty $, have spectra [0, ∞). In this note, we provide an alternative and elementary proof of this result. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)