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

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.