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Mat. Zametki, 2005, Volume 78, Issue 1, Pages 72–84 (Mi mz2563)  

This article is cited in 12 scientific papers (total in 12 papers)

Necessary Conditions for the Localization of the Spectrum of the Sturm–Liouville Problem on a Curve

Kh. K. Ishkin

Bashkir State University

Abstract: Abstract We consider the Sturm–Liouville operator on a convex smooth curve lying in the complex plane and connecting the points 0 and 1. We prove that if the eigenvalues $\lambda_k$ with large numbers are localized near a single ray, then this ray is the positive real semiaxis. Moreover, if the eigenvalues $\lambda_k$ are numbered with algebraic multiplicities taken into account, then $\lambda_k\sim\pi\cdot k$, $k\to+\infty$.

DOI: https://doi.org/10.4213/mzm2563

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English version:
Mathematical Notes, 2005, 78:1, 64–75

Bibliographic databases:

UDC: 517.927.25
Received: 14.11.2003
Revised: 25.10.2004

Citation: Kh. K. Ishkin, “Necessary Conditions for the Localization of the Spectrum of the Sturm–Liouville Problem on a Curve”, Mat. Zametki, 78:1 (2005), 72–84; Math. Notes, 78:1 (2005), 64–75

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kh. K. Ishkin, “On the Uniqueness Criterion for Solutions of the Sturm–Liouville Equation”, Math. Notes, 84:4 (2008), 515–528  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Ishkin Kh.K., “Conditions for Localization of the Limit Spectrum of a Model Operator Associated with the Orr-Sommerfeld Equation”, Dokl. Math., 86:1 (2012), 549–552  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. Kh. K. Ishkin, “On analytic properties of Weyl function of Sturm–Liouville operator with a decaying complex potential”, Ufa Math. J., 5:1 (2013), 36–55  mathnet  crossref  mathscinet  elib
    4. Ishkin Kh.K., “on the Birkhoff-Tamarkin-Langer Conditions and a Conjecture of Davies”, Dokl. Math., 91:3 (2015), 259–262  crossref  mathscinet  zmath  isi  elib  scopus
    5. Kh. K. Ishkin, “Localization criterion for the spectrum of the Sturm–Liouville operator on a curve”, St. Petersburg Math. J., 28:1 (2017), 37–63  mathnet  crossref  mathscinet  isi  elib
    6. A. A. Golubkov, “Obratnaya zadacha dlya operatorov Shturma–Liuvillya v kompleksnoi ploskosti”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 18:2 (2018), 144–156  mathnet  crossref  elib
    7. Kh. K. Ishkin, A. V. Rezbaev, “K formule Devisa o raspredelenii sobstvennykh chisel nesamosopryazhennogo differentsialnogo operatora”, Kompleksnyi analiz, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 153, VINITI RAN, M., 2018, 84–93  mathnet  mathscinet
    8. A. A. Golubkov, “Asymptotics of transfer matrix of Sturm–Liouville equation with piecewise-entire potential function on a curve”, Moscow University Mathematics Bulletin, 74:2 (2019), 65–69  mathnet  crossref  mathscinet  zmath  isi
    9. Golubkov A.A. Kuryshova Yu.V., “Inverse Problem For Sturm-Liouville Operators on a Curve”, Tamkang J. Math., 50:3, SI (2019), 349–359  crossref  mathscinet  isi
    10. Kh. K. Ishkin, R. I. Marvanov, “Equivalence criterion for two asymptotic formulae”, Ufa Math. J., 12:1 (2020), 30–42  mathnet  crossref  isi
    11. Kh. K. Ishkin, R. I. Marvanov, “On localization conditions for spectrum of model operator for Orr–Sommerfeld equation”, Ufa Math. J., 12:4 (2020), 64–77  mathnet  crossref  isi
    12. Ishkin Kh.K. Davletova L.G., “Regularized Trace of a Sturm-Liouville Operator on a Curve With a Regular Singularity on the Chord”, Differ. Equ., 56:10 (2020), 1257–1269  crossref  mathscinet  isi
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