Asymptotic analysis of non-self-adjoint Hill operators

• Autorzy: Oktay Veliev
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Asymptotic formulas; Hill operator; Spectral singularities; Spectral operator

Kategorie tematyczne

• 34L20: Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions
• 34L05: General spectral theory

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 12
• Strony: 2234-2256

Daty

wydano

2013-12-01

online

2013-10-08

Twórcy

autor

Oktay Veliev

• Doğuş University

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0305-x