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

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Matematicheskie Zametki, 2008, Volume 83, Issue 1, Pages 139–152
DOI: https://doi.org/10.4213/mzm4340 (Mi mzm4340)

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

Inverse Problems for Differential Operators of Any Order on Trees

V. A. Yurko

Saratov State University named after N. G. Chernyshevsky

Full-text PDF (520 kB) Citations (22)

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

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.

Received: 19.04.2007

English version:
Mathematical Notes, 2008, Volume 83, Issue 1, Pages 125–137
DOI: https://doi.org/10.1134/S000143460801015X

Bibliographic databases:

UDC: 517.984

Language: Russian

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

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Linking options:

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https://doi.org/10.4213/mzm4340

https://www.mathnet.ru/eng/mzm/v83/i1/p139

This publication is cited in the following 22 articles:

Vasiliev S.V., “An Inverse Spectral Problem For Sturm-Liouville Operators With Singular Potentials on Arbitrary Compact Graphs”, Tamkang J. Math., 50:3, SI (2019), 293–305
V. A. Yurko, “Inverse spectral problems for differential operators on spatial networks”, Russian Math. Surveys, 71:3 (2016), 539–584
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
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
Yurko V., “Inverse Problems For Differential Operators of Variable Orders on Star-Type Graphs: General Case”, Anal. Math. Phys., 4:3 (2014), 247–262
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
Yurko V.A., “Recovering Variable Order Differential Operators on Star-Type Graphs From Spectra”, Differ. Equ., 49:12 (2013), 1490–1501
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
Yurko V.A., “Inverse spectral problems for arbitrary order differential operators on noncompact trees”, J. Inverse Ill-Posed Probl., 20:1 (2012), 111–131
V. A. Yurko, “Inverse Problem for Sturm–Liouville Operators on Hedgehog-Type Graphs”, Math. Notes, 89:3 (2011), 438–449
Yurko V.A., “Reconstruction of Sturm-Liouville differential operators on A-graphs”, Differ. Equ., 47:1 (2011), 50–59
Freiling G., Ignatyev M., “Spectral analysis for the Sturm-Liouville operator on sun-type graphs”, Inverse Problems, 27:9 (2011), 095003, 17 pp.
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
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
Yurko V.A., “Inverse spectral problems for differential operators on arbitrary compact graphs”, J. Inverse Ill-Posed Probl., 18:3 (2010), 245–261
Yurko V. A., “An inverse spectral problem for differential operators on a hedgehog-type graph”, Dokl. Math., 79:2 (2009), 250–254
V. A. Yurko, “Recovering Sturm-Liouville operators from spectra on a graph with a cycle”, Sb. Math., 200:9 (2009), 1403–1415
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
Yurko V., “Uniqueness of recovering Sturm-Liouville operators on $A$ -graphs from spectra”, Results Math., 55:1-2 (2009), 199–207
Yurko V., “Inverse problems for Sturm-Liouville operators on bush-type graphs”, Inverse Problems, 25:10 (2009), 105008, 14 pp.

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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