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Algebra i Analiz, 2009, Volume 21, Issue 5, Pages 114–137 (Mi aa1155)  

This article is cited in 18 scientific papers (total in 18 papers)

Research Papers

The inverse Sturm–Liouville problem with mixed boundary conditions

E. L. Korotyaeva, D. S. Chelkakb

a School of Math., Cardiff University, Cardiff, Wales, UK
b St. Petersburg State University, Department of Mathematics and Mechanics, St. Petersburg, Russia
References:
Abstract: Let Hψ=ψ+qψ, ψ(0)=0, ψ(1)+bψ(1)=0 be a selfadjoint Sturm-Liouville operator acting in L2(0,1). Let λn(q,b) and νn(q,b) denote its eigenvalues and the so-called norming constants, respectively. A complete characterization of all spectral data ({λn}+n=0;{νn}+n=0) corresponding to (q;b)L2(0,1)×R is given, together with a similar characterization for fixed b and a parametrization of isospectral manifolds.
Received: 15.03.2008
English version:
St. Petersburg Mathematical Journal, 2010, Volume 21, Issue 5, Pages 761–778
DOI: https://doi.org/10.1090/S1061-0022-2010-01116-6
Bibliographic databases:
Document Type: Article
MSC: 34B24
Language: Russian
Citation: E. L. Korotyaev, D. S. Chelkak, “The inverse Sturm–Liouville problem with mixed boundary conditions”, Algebra i Analiz, 21:5 (2009), 114–137; St. Petersburg Math. J., 21:5 (2010), 761–778
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/aa1155
  • https://www.mathnet.ru/eng/aa/v21/i5/p114
  • This publication is cited in the following 18 articles:
    1. Namig J. Guliyev, “Spectral identities for Schrödinger operators”, Can. Math. Bull., 2025, 1  crossref
    2. Korotyaev E.L., “Eigenvalues of Schrodinger Operators on Finite and Infinite Intervals”, Math. Nachr., 294:11 (2021), 2188–2199  crossref  mathscinet  isi
    3. Hameed E.M., Al-Jaberi A.K., “The Convergent Sequence to the Weighted Operator”, Ital. J. Pure Appl. Math., 2021, no. 46, 548–556  isi
    4. Guliyev N.J., “Essentially Isospectral Transformations and Their Applications”, Ann. Mat. Pura Appl., 199:4 (2020), 1621–1648  crossref  mathscinet  isi
    5. V. A. Sadovnichii, Ya. T. Sultanaev, A. M. Akhtyamov, “Uniqueness of reconstruction of an $n$th-order differential operator with nonseparated boundary conditions by several spectra”, Dokl. Math., 101:1 (2020), 46–48  mathnet  crossref  crossref  zmath  elib
    6. Hiroshi Isozaki, SpringerBriefs in Mathematical Physics, 38, Inverse Spectral and Scattering Theory, 2020, 1  crossref
    7. Sadovnichii V.A., Sultanaev Ya.T., Akhtyamov A.M., “Inverse Sturm-Liouville Problem With Nonseparated Boundary Conditions on a Geometric Graph”, Differ. Equ., 55:2 (2019), 194–204  crossref  mathscinet  isi  scopus
    8. Korotyaev E.L., “Inverse Sturm-Liouville Problems For Non-Borg Conditions”, J. Inverse Ill-Posed Probl., 27:3 (2019), 445–452  crossref  mathscinet  isi
    9. 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  mathscinet  isi  scopus
    10. V. A. Sadovnichii, Ya. T. Sultanaev, A. M. Akhtyamov, “Inverse problem for a differential operator with nonseparated boundary conditions”, Dokl. Math., 97:2 (2018), 181–183  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus
    11. Sadovnichy V.A., Sultanaev Ya.T., Aklityamov A.M., “On the Uniqueness of the Solution of the Inverse Sturm-Liouville Problem With Nonseparated Boundary Conditions on a Geometric Graph”, Dokl. Math., 98:1 (2018), 338–340  crossref  mathscinet  zmath  isi  scopus
    12. Sadovnichii V.A., Sultanaev Ya.T., Akhtyamov A.M., “Inverse Problem For a Fourth-Order Differential Operator With Nonseparated Boundary Conditions”, Differ. Equ., 54:10 (2018), 1354–1362  crossref  mathscinet  zmath  isi  scopus
    13. A. M. Akhtyamov, I. M. Utyashev, “Vosstanovlenie polinomialnogo potentsiala v zadache Shturma–Liuvillya”, Zhurnal SVMO, 20:2 (2018), 148–158  mathnet  crossref
    14. Isozaki H., Korotyaev E.L., “Global transformations preserving Sturm–Liouville spectral data”, Russ. J. Math. Phys., 24:1 (2017), 51–68  crossref  mathscinet  zmath  isi  scopus
    15. Guo H., Qi J., “Extremal Norm For Potentials of Sturm-Liouville Eigenvalue Problems With Separated Boundary Conditions”, Electron. J. Differ. Equ., 2017, 99  mathscinet  isi  elib
    16. Isozaki H., Korotyaev E.L., “Inverse Spectral Theory and the Minkowski Problem For the Surface of Revolution”, Dyn. Partial Differ. Equ., 14:4 (2017), 321–341  crossref  mathscinet  zmath  isi
    17. Ibadzadeh Ch.G., Nabiev I.M., “An inverse problem for Sturm–Liouville operators with non-separated boundary conditions containing the spectral parameter”, J. Inverse Ill-Posed Probl., 24:4 (2016), 407–411  crossref  mathscinet  zmath  isi  elib  scopus
    18. A. M. Savchuk, A. A. Shkalikov, “Inverse Problems for Sturm–Liouville Operators with Potentials in Sobolev Spaces: Uniform Stability”, Funct. Anal. Appl., 44:4 (2010), 270–285  mathnet  crossref  crossref  mathscinet  zmath  isi
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