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Mat. Zametki, 2008, Volume 83, Issue 1, Pages 139–152 (Mi mz4340)  

This article is cited in 21 scientific papers (total in 21 papers)

Inverse Problems for Differential Operators of Any Order on Trees

V. A. Yurko

Saratov State University named after N. G. Chernyshevsky

Abstract: Inverse spectral problems for ordinary differential operators of any order on compact trees are studied. As the main spectral characteristics, Weyl matrices, which generalize the Weyl $m$-function for the classical Sturm–Liouville operator are introduced and studied. A constructive solution procedure for the inverse problem based on Weyl matrices is suggested, and the uniqueness of the solution is proved. The reconstruction of differential equations from discrete spectral characteristics is also considered.

Keywords: differential operator on a tree, inverse spectral problem on a tree, Weyl solution, Weyl matrix, method of spectral mappings

DOI: https://doi.org/10.4213/mzm4340

Full text: PDF file (520 kB)
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English version:
Mathematical Notes, 2008, 83:1, 125–137

Bibliographic databases:

UDC: 517.984
Received: 19.04.2007

Citation: V. A. Yurko, “Inverse Problems for Differential Operators of Any Order on Trees”, Mat. Zametki, 83:1 (2008), 139–152; Math. Notes, 83:1 (2008), 125–137

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yurko V. A., “Inverse problems for Sturm-Liouville operators on graphs with a cycle”, Oper. Matrices, 2:4 (2008), 543–553  crossref  mathscinet  zmath  isi
    2. Yurko V. A., “An inverse spectral problem for differential operators on a hedgehog-type graph”, Dokl. Math., 79:2 (2009), 250–254  mathnet  crossref  mathscinet  mathscinet  zmath  isi  elib  elib  scopus
    3. V. A. Yurko, “Recovering Sturm-Liouville operators from spectra on a graph with a cycle”, Sb. Math., 200:9 (2009), 1403–1415  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Yurko V. A., “Inverse spectral problems for Sturm-Liouville differential operators on a finite interval”, J. Inverse Ill-Posed Probl., 17:7 (2009), 639–694  crossref  mathscinet  zmath  isi  elib  scopus
    5. Yurko V., “Uniqueness of recovering Sturm-Liouville operators on $A$-graphs from spectra”, Results Math., 55:1-2 (2009), 199–207  crossref  mathscinet  zmath  isi  elib  scopus
    6. Yurko V., “Inverse problems for Sturm-Liouville operators on bush-type graphs”, Inverse Problems, 25:10 (2009), 105008, 14 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    7. V. A. Yurko, “Vosstanovlenie differentsialnykh operatorov na grafe-kuste”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 9:2 (2009), 59–65  mathnet  elib
    8. V. A. Yurko, “Edinstvennost resheniya obratnoi zadachi dlya differentsialnykh operatorov na proizvolnykh kompaktnykh grafakh”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 10:3 (2010), 33–38  mathnet
    9. Avdonin S., Kurasov P., Nowaczyk M., “Inverse problems for quantum trees II: recovering matching conditions for star graphs”, Inverse Probl. Imaging, 4:4 (2010), 579–598  crossref  mathscinet  zmath  isi  elib  scopus
    10. Yurko V.A., “Inverse spectral problems for differential operators on arbitrary compact graphs”, J. Inverse Ill-Posed Probl., 18:3 (2010), 245–261  crossref  mathscinet  zmath  isi  elib  scopus
    11. V. A. Yurko, “Inverse Problem for Sturm–Liouville Operators on Hedgehog-Type Graphs”, Math. Notes, 89:3 (2011), 438–449  mathnet  crossref  crossref  mathscinet  isi
    12. Yurko V.A., “Reconstruction of Sturm-Liouville differential operators on A-graphs”, Differ. Equ., 47:1 (2011), 50–59  crossref  mathscinet  zmath  isi  elib  elib  scopus
    13. Freiling G., Ignatyev M., “Spectral analysis for the Sturm-Liouville operator on sun-type graphs”, Inverse Problems, 27:9 (2011), 095003, 17 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    14. V. A. Yurko, “Edinstvennost vosstanovleniya differentsialnykh operatorov proizvolnykh poryadkov na nekompaktnykh prostranstvennykh setyakh”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 12:2 (2012), 33–41  mathnet
    15. Yurko V.A., “Inverse spectral problems for arbitrary order differential operators on noncompact trees”, J. Inverse Ill-Posed Probl., 20:1 (2012), 111–131  crossref  mathscinet  zmath  isi  elib  scopus
    16. Pikula M., Vladicic V., Markovic O., “A Solution to the Inverse Problem for the Sturm-Liouville-Type Equation with a Delay”, Filomat, 27:7 (2013), 1237–1245  crossref  mathscinet  zmath  isi  scopus
    17. Yurko V.A., “Recovering Variable Order Differential Operators on Star-Type Graphs From Spectra”, Differ. Equ., 49:12 (2013), 1490–1501  crossref  mathscinet  zmath  isi  scopus
    18. Yurko V., “Inverse Problems on Star-Type Graphs: Differential Operators of Different Orders on Different Edges”, Cent. Eur. J. Math., 12:3 (2014), 483–499  crossref  mathscinet  zmath  isi  scopus
    19. Yurko V., “Inverse Problems For Differential Operators of Variable Orders on Star-Type Graphs: General Case”, Anal. Math. Phys., 4:3 (2014), 247–262  crossref  mathscinet  zmath  isi  scopus
    20. A. A. Sedipkov, “Recovery of the discontinuities of the coefficient of a Sturm–Liouville operator in impedance form”, Siberian Math. J., 56:2 (2015), 367–372  mathnet  crossref  mathscinet  isi  elib  elib
    21. V. A. Yurko, “Inverse spectral problems for differential operators on spatial networks”, Russian Math. Surveys, 71:3 (2016), 539–584  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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