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Izv. RAN. Ser. Mat., 2010, Volume 74, Issue 3, Pages 3–22 (Mi izv2669)  

This article is cited in 3 scientific papers (total in 3 papers)

The eigenvalue function of a family of Sturm–Liouville operators

T. N. Harutyunyan

Yerevan State University

Abstract: We define a function $\mu^-(\gamma)$ in such a way that its value at every point $\gamma\in(-\infty,\pi)$, $\gamma=\beta-\pi n$, $\beta\in[0,\pi)$, $n=0,1,2,…$, coincides with an eigenvalue $\mu_n(\alpha,\beta)$ of the Sturm–Liouville problem $-y"+q(x)y=\mu y$, $y(0)\cos\alpha+y'(0)\sin\alpha=0$, $y(\pi)\cos\beta+y'(\pi)\sin\beta=0$ (for some $\alpha {\in} (0,\pi]$). We find necessary and sufficient conditions for a function to have this property for a real $q\in L^1[0,\pi]$.

Keywords: Sturm–Liouville problem, eigenvalue function, inverse problem.

DOI: https://doi.org/10.4213/im2669

Full text: PDF file (559 kB)
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English version:
Izvestiya: Mathematics, 2010, 74:3, 439–459

Bibliographic databases:

UDC: 517.9
MSC: 34A55, 34B20, 34E99, 34L99, 35Q99, 37A30, 47E05, 58C40
Received: 25.05.2007
Revised: 07.04.2008

Citation: T. N. Harutyunyan, “The eigenvalue function of a family of Sturm–Liouville operators”, Izv. RAN. Ser. Mat., 74:3 (2010), 3–22; Izv. Math., 74:3 (2010), 439–459

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. Yu. A. Ashrafyan, T. N. Harutyunyan, “Inverse Sturm-Liouville problems with fixed boundary conditions”, Electron. J. Differential Equations, 2015, 27, 8 pp.  mathscinet  zmath  isi
    2. Harutyunyan T., “Uniqueness Theorem For the Eigenvalues' Function”, Lobachevskii J. Math., 40:8, SI (2019), 1079–1083  crossref  isi
    3. Harutyunyan T., “the Eigenvalues' Function of the Family of Sturm-Liouville Operators and the Inverse Problems”, Tamkang J. Math., 50:3, SI (2019), 233–252  crossref  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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