Asymptotics for eigenvalues of Sturm–Liouville operator with periodic boundary conditions

Abstract

We employ the similar operators method for studying the spectral properties of the Sturm–Liouville operator generated by the differential expression $l(y)=-y''-vy$ with a complex potential $v$ and subject to periodic boundary conditions $y(0)=y(2\pi)$, $y'(0)=y'(2\pi)$. We obtain the results on the asymptotics for the spectrum of the operator.