# Asymptotic analysis of non-self-adjoint Hill operators

Open Mathematics (2013)

- Volume: 11, Issue: 12, page 2234-2256
- ISSN: 2391-5455

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topOktay Veliev. "Asymptotic analysis of non-self-adjoint Hill operators." Open Mathematics 11.12 (2013): 2234-2256. <http://eudml.org/doc/269430>.

@article{OktayVeliev2013,

abstract = {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.},

author = {Oktay Veliev},

journal = {Open Mathematics},

keywords = {Asymptotic formulas; Hill operator; Spectral singularities; Spectral operator; asymptotic formulas; spectral singularities; spectral operator},

language = {eng},

number = {12},

pages = {2234-2256},

title = {Asymptotic analysis of non-self-adjoint Hill operators},

url = {http://eudml.org/doc/269430},

volume = {11},

year = {2013},

}

TY - JOUR

AU - Oktay Veliev

TI - Asymptotic analysis of non-self-adjoint Hill operators

JO - Open Mathematics

PY - 2013

VL - 11

IS - 12

SP - 2234

EP - 2256

AB - 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.

LA - eng

KW - Asymptotic formulas; Hill operator; Spectral singularities; Spectral operator; asymptotic formulas; spectral singularities; spectral operator

UR - http://eudml.org/doc/269430

ER -

## References

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