Asymptotic Analysis of Non-self-adjoint Hill Operators

O. A. Veliev

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arXiv · 1107.2552

Asymptotic Analysis of Non-self-adjoint Hill Operators

O. A. Veliev

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Abstract

We obtain the uniform asymptotic formulas for the eigenvalues and eigenfunctions of the Sturm-Liouville operators L_{t}(q) with a potential q\inL_{1}[0,1] and with t-periodic boundary conditions, t\in(-{\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}(-\infty,\infty) 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 the sufficient conditions.

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BibTeX RIS

O. A. Veliev. 2011-07-13. Asymptotic Analysis of Non-self-adjoint Hill Operators. https://arxiv.org/abs/1107.2552

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