# 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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## Abstract

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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.

## How to cite

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Oktay 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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