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Inverse Spectral Problems for Differential Pencils on Arbitrary Compact Graphs

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Abstract

Inverse problems of spectral analysis are studied for second-order differential pencils on arbitrary compact graphs. The uniqueness of recovering operators from their spectra is proved, and a constructive procedure for the solution of this class of inverse problems is provided.

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References

  1. Pokorny, Yu.V., Penkin, O.M., Pryadiev, V.L., Borovskikh A.V., Lazarev, K.P., Shabrov, C.A., Differentsial’nye uravneniya na geometricheskikh grafakh (Differential Equations on Geometric Graphs), Moscow: Fizmatlit, 2004.

    Google Scholar 

  2. Marchenko, V.A., Operatory Shturma–Liuvillya i ikh prilozheniya, Kiev: Naukova Dumka, 1977. Translated under the title Sturm–Liouville Operators and Their Applications, Birkhäuser, 1986.

    Google Scholar 

  3. Levitan, B.M., Obratnye zadachi Shturma–Liuvillya, Moscow: Nauka, 1984. Translated under the title Inverse Sturm–Liouville Problems, Utrecht: VNU Sci. Press, 1987.

    MATH  Google Scholar 

  4. Freiling, G. and Yurko, V.A., Inverse Sturm–Liouville Problems and Their Applications, New York: NOVA Science Publishers, 2001.

    MATH  Google Scholar 

  5. Yurko, V.A., Method of Spectral Mappings in the Inverse Problem Theory, Inverse and Ill-Posed Problems Series, Utrecht: VSP, 2002.

    Book  MATH  Google Scholar 

  6. Yurko, V.A., Vvedenie v teoriyu obratnykh spektral’nykh zadach (Introduction to the Theory of Inverse Spectral Problems), Moscow: Fizmatlit, 2007.

    Google Scholar 

  7. Belishev, M.I., Boundary spectral inverse problem on a class of graphs (trees) by the BC method, Inverse Problems, 2004, vol. 20, pp. 647–672.

    Article  MathSciNet  MATH  Google Scholar 

  8. Yurko, V.A., Inverse spectral problems for Sturm–Liouville operators on graphs, Inverse Problems, 2005, vol. 21, no. 3, pp. 1075–1086.

    Article  MathSciNet  MATH  Google Scholar 

  9. Brown, B.M. and Weikard, R., A Borg–Levinson theorem for trees, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 2005, vol. 461, no. 2062, pp. 3231–3243.

    Article  MathSciNet  MATH  Google Scholar 

  10. Yang, C-Fu and Yang, X-P., Uniqueness theorems from partial information of the potential on a graph, J. Inverse Ill-Posed Problems, 2011, vol. 19, no. 4–5, pp. 631–639.

    Book  MATH  Google Scholar 

  11. Yurko, V.A., Reconstruction of Sturm–Liouville differential operators on A-graphs, Differ. Equations, 2011, vol. 47, no. 1, pp. 50–59.

    Article  MathSciNet  MATH  Google Scholar 

  12. Yurko, V.A., Inverse spectral problems for differential operators on arbitrary compact graphs, J. Inverse Ill-Posed Proplems, 2010, vol. 18, no. 3, pp. 245–261.

    MathSciNet  MATH  Google Scholar 

  13. Yurko, V.A., An inverse problem for differential pencils on graphs with a cycle, J. Inverse Ill-Posed Problems, 2014, vol. 22, no. 5, pp. 625–641.

    Article  MathSciNet  MATH  Google Scholar 

  14. Yurko, V.A., Inverse problem for differential pencils on hedgehog-graphs, Differ. Equations, 2016, vol. 52, no. 3, pp. 335–345.

    Article  MathSciNet  MATH  Google Scholar 

  15. Mennicken, R. and Möller, M., Non-Self-Adjoint Boundary Value Problems, North-Holland Mathematic Studies, Vol. 192, Amsterdam: North-Holland, 2003.

    Google Scholar 

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Correspondence to V. Yurko.

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Russian Text © V. Yurko, 2019, published in Differentsial’nye Uravneniya, 2019, Vol. 55, No. 1, pp. 25–33.

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Yurko, V. Inverse Spectral Problems for Differential Pencils on Arbitrary Compact Graphs. Diff Equat 55, 24–33 (2019). https://doi.org/10.1134/S0012266119010038

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  • DOI: https://doi.org/10.1134/S0012266119010038

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