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Mat. Zametki, 2006, Volume 79, Issue 4, Pages 619–630 (Mi mz2732)  

This article is cited in 22 scientific papers (total in 22 papers)

On recovering Sturm–Liouville operators on graphs

V. A. Yurko

Saratov State University named after N. G. Chernyshevsky

Abstract: Sturm–Liouville differential operators on compact graphs are studied. We establish properties of the spectral characteristics and investigate three inverse problems of recovering the operator from the so-called Weyl functions, from discrete spectral data, and from a system of spectra. For these inverse problems, we prove uniqueness theorems and obtain procedures for constructing the solutions by the method of spectral mappings.


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English version:
Mathematical Notes, 2006, 79:4, 572–582

Bibliographic databases:

UDC: 517.984
Received: 16.02.2005

Citation: V. A. Yurko, “On recovering Sturm–Liouville operators on graphs”, Mat. Zametki, 79:4 (2006), 619–630; Math. Notes, 79:4 (2006), 572–582

Citation in format AMSBIB
\by V.~A.~Yurko
\paper On recovering Sturm--Liouville operators on graphs
\jour Mat. Zametki
\yr 2006
\vol 79
\issue 4
\pages 619--630
\jour Math. Notes
\yr 2006
\vol 79
\issue 4
\pages 572--582

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    This publication is cited in the following articles:
    1. Freiling G., Yurko V., “Inverse problems for Sturm-Liouville operators on noncompact trees”, Results Math., 50:3-4 (2007), 195–212  crossref  mathscinet  isi  elib  scopus
    2. Yurko V.A., “An inverse problem for higher order differential operators on star-type graphs”, Inverse Problems, 23:3 (2007), 893–903  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Currie S., Watson B.A., “Green's functions and regularized traces of Sturm-Liouville operators on graphs”, Proc. Edinb. Math. Soc. (2), 51:2 (2008), 315–335  crossref  mathscinet  zmath  isi  scopus
    4. Kurasov P., “Schrodinger operators on graphs and geometry I: Essentially bounded potentials”, J. Funct. Anal., 254:4 (2008), 934–953  crossref  mathscinet  zmath  isi  elib  scopus
    5. Yurko V., “Recovering differential pencils on compact graphs”, J. Differential Equations, 244:2 (2008), 431–443  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. Yurko V.A., “Inverse spectral problem for differential operator pencils on noncompact spatial networks”, Differ. Equ., 44:12 (2008), 1721–1729  crossref  zmath  isi  elib  scopus
    7. Frenling G. Ignatiev M. Yurko V., “An Inverse Spectral Problem for Sturm-Liouville Operators with. Singular Potentials on Star-Type Graphs”, Analysis on Graphs and its Applications, Proceedings of Symposia in Pure Mathematics, 77, ed. Exner P. Keating J. Kuchment P. Sunada T. Teplyaev A., Amer Mathematical Soc, 2008, 397–408  crossref  mathscinet  isi
    8. Kurasov P., “On the inverse problem for quantum graphs with one cycle”, Acta Physica Polonica A, 116:5 (2009), 765–771  crossref  adsnasa  isi  elib  scopus
    9. O. V. Korovina, V. L. Pryadiev, “Struktura resheniya smeshannoi zadachi dlya volnovogo uravneniya na kompaktnom geometricheskom grafe v sluchae nenulevoi nachalnoi skorosti”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 9:3 (2009), 37–46  mathnet  crossref
    10. Kurasov P., “Inverse problems for Aharonov-Bohm rings”, Math. Proc. Cambridge Philos. Soc., 148:2 (2010), 331–362  crossref  mathscinet  zmath  isi  elib  scopus
    11. Yang Chuan-Fu, “Inverse spectral problems for the Sturm-Liouville operator on a $d$-star graph”, J. Math. Anal. Appl., 365:2 (2010), 742–749  crossref  mathscinet  zmath  isi  elib  scopus
    12. Avdonin S., Kurasov P., Nowaczyk M., “Inverse problems for quantum trees II: recovering matching conditions for star graphs”, Inverse Problems and Imaging, 4:4 (2010), 579–598  crossref  mathscinet  zmath  isi  scopus
    13. Yang Ch.-F., Huang Zh.-Y., Yang X.-P., “Trace formulae for Schrödinger systems on graphs”, Turkish J. Math., 34:2 (2010), 181–196  mathscinet  zmath  isi  elib
    14. Kurasov P., “Inverse Problems for Quantum Graphs: Recent Developments and Perspectives”, Acta Phys. Pol. A, 120:6A, SI (2011), A132–A141  crossref  isi
    15. Kurasov P., Enerback M., “Aharonov-Bohm Ring Touching a Quantum Wire: How to Model It and to Solve the Inverse Problem”, Rep. Math. Phys., 68:3 (2011), 271–287  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    16. Yang Ch.-F., Yang X.-P., “Uniqueness Theorems From Partial Information of the Potential on a Graph”, J. Inverse Ill-Posed Probl., 19:4-5 (2011), 631–641  crossref  mathscinet  zmath  isi  scopus
    17. Kurasov P., “Can One Distinguish Quantum Trees From the Boundary?”, Proc. Amer. Math. Soc., 140:7 (2012), 2347–2356  crossref  mathscinet  zmath  isi  elib  scopus
    18. Kurasov P., “Inverse Scattering for Lasso Graph”, J. Math. Phys., 54:4 (2013), 042103  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    19. L. K. Zhapsarbayeva, B. E. Kanguzhin, M. N. Konyrkulzhayeva, “Self-adjoint restrictions of maximal operator on graph”, Ufa Math. J., 9:4 (2017), 35–43  mathnet  crossref  isi  elib
    20. Bondarenko N., Shieh Ch.-Ts., “Partial Inverse Problems For Sturm-Liouville Operators on Trees”, Proc. R. Soc. Edinb. Sect. A-Math., 147:5 (2017), 917–933  crossref  mathscinet  zmath  isi  scopus
    21. M. A. Kuznetsova, “Asymptotic formulae for weight numbers of the Sturm–Liouville boundary problem on a star-shaped graph”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 18:1 (2018), 40–48  mathnet  crossref  elib
    22. S. V. Vasilev, “An inverse spectral problem for Sturm–Liouville operators with singular potentials on graphs with a cycle”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 19:4 (2019), 366–376  mathnet  crossref
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