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.
Keywords:similar operators method, Sturm–Liouville operator, the spectrum of operator, asymptotics for the spectrum.