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Asymptotic analysis of non-self-adjoint Hill operators

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Veliev O.

Open Mathematics

2013

tom 11

nr 12

2234-2256

We obtain uniform asymptotic formulas for the eigenvalues and eigenfunctions of the Sturm-Liouville operators L t (q) with a potential q ∈ L 1[0,1] and t-periodic boundary conditions, t ∈ (−π, π]. 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(−∞,∞) 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.

Ograniczanie wyników

1 Open Mathematics

1 Veliev O.

1 2013

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Asymptotic analysis of non-self-adjoint Hill operators