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Mat. Zametki, 2013, Volume 94, Issue 4, Pages 552–568 (Mi mz10319)  

This article is cited in 4 scientific papers (total in 4 papers)

On a Trivial Monodromy Criterion for the Sturm–Liouville Equation

Kh. K. Ishkin

Bashkir State University, Ufa

Abstract: We obtain a necessary and sufficient condition for the equation $-y"(z)+q(z)y(z)=\lambda y(z)$ to be monodromy-free; here $z\in \gamma$ and $\gamma$ is a piecewise smooth curve which is the boundary of a convex bounded domain.

Keywords: Sturm–Liouville equation, monodromy-free potential, meromorphic function, monodromy matrix, Sokhotskii–Plemelj formula, Gronwall inequality, Hardy class.

DOI: https://doi.org/10.4213/mzm10319

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English version:
Mathematical Notes, 2013, 94:4, 508–523

Bibliographic databases:

UDC: 517.925
Received: 24.04.2013

Citation: Kh. K. Ishkin, “On a Trivial Monodromy Criterion for the Sturm–Liouville Equation”, Mat. Zametki, 94:4 (2013), 552–568; Math. Notes, 94:4 (2013), 508–523

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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. 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
    2. 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
    3. Kh. K. Ishkin, “Conditions of spectrum localization for operators not close to self-adjoint operators”, Dokl. Math., 97:2 (2018), 170–173  mathnet  crossref  crossref  zmath  isi  elib  scopus
    4. 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
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