Asymptotic analysis of non - self - adjoint Hill operators
YazarVeliev, Oktay A.
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KünyeVELİEV, O. (2013). Asymptotic analysis of non - self - adjoint Hill operators. Central European Journal of Mathematics, 11 (12), pp. 2234-2256. http://dx.doi.org/10.2478/s11533-013-0305-x.
We obtain uniform asymptotic formulas for the eigenvalues and eigenfunctions of the Sturm-Liouville operators L (t) (q) with a potential q a L (1)[0,1] and t-periodic boundary conditions, t a (-pi, pi]. Using these formulas, we find sufficient conditions on the potential q such that the number of spectral singularities in the spectrum of the Hill operator L(q) in L (2)(-a,a) is finite. Then we prove that the operator L(q) has no spectral singularities at infinity and it is an asymptotically spectral operator provided that the potential q satisfies sufficient conditions.