A partial inverse problem for quantum graphs with a loop

References

[1] N. P. Bondarenko, A 2-edge partial inverse problem for the Sturm–Liouville operators with singular potentials on a star-shaped graph, Tamkang J. Math. 49 (2018), no. 1, 49–66. 10.5556/j.tkjm.49.2018.2425Search in Google Scholar

[2] N. P. Bondarenko, A partial inverse problem for the Sturm–Liouville operator on a star-shaped graph, Anal. Math. Phys. 8 (2018), no. 1, 155–168. 10.1007/s13324-017-0172-xSearch in Google Scholar

[3] N. P. Bondarenko, Partial inverse problems for the Sturm–Liouville operator on a star-shaped graph with mixed boundary conditions, J. Inverse Ill-Posed Probl. 26 (2018), no. 1, 1–12. 10.1515/jiip-2017-0001Search in Google Scholar

[4] N. P. Bondarenko and C.-T. Shieh, Partial inverse problems for quadratic differential pencils on a graph with a loop, J. Inverse Ill-Posed Probl. 28 (2020), no. 3, 449–463. 10.1515/jiip-2018-0104Search in Google Scholar

[5] P. Exner, J. P. Keating, P. Kuchment, T. Sunada and A. Teplyaev, Vladimir A. Geyler, April 29, 1943–April 2, 2007, Analysis on Graphs and its Applications, Proc. Sympos. Pure Math. 77, American Mathematical Society, Providence (2008), 1–8. Search in Google Scholar

[6] G. Freiling and V. Yurko, Inverse Sturm–Liouville Problems and Their Applications, Nova Science, Huntington, 2001. Search in Google Scholar

[7] O. H. Hald, Discontinuous inverse eigenvalue problems, Comm. Pure Appl. Math. 37 (1984), no. 5, 539–577. 10.1002/cpa.3160370502Search in Google Scholar

[8] X. He and H. Volkmer, Riesz bases of solutions of Sturm–Liouville equations, J. Fourier Anal. Appl. 7 (2001), no. 3, 297–307. 10.1007/BF02511815Search in Google Scholar

[9] P. Kuchment, Graph models for waves in thin structures, Waves Random Media 12 (2002), no. 4, R1–R24. 10.1088/0959-7174/12/4/201Search in Google Scholar

[10] P. Kuchment, Quantum graphs. I. Some basic structures, Waves Random Media 14 (2004), S107–S128. 10.1088/0959-7174/14/1/014Search in Google Scholar

[11] P. Kurasov, On the inverse problem for quantum graphs with one cycle, Acta Phys. Polon. A. 116 (2009), no. 5, 765–771. 10.12693/APhysPolA.116.765Search in Google Scholar

[12] B. M. Levitan, Inverse Sturm–Liouville Problems, (in Russian), “Nauka”, Moscow, 1984. Search in Google Scholar

[13] V. A. Marchenko, Sturm–Liouville Operators and their Applications, (in Russian), Izdat. “Naukova Dumka”, Kiev, 1977. Search in Google Scholar

[14] E. W. Montroll, Quantum theory on a network. I. A solvable model whose wavefunctions are elementary functions, J. Math. Phys. 11 (1970), no. 2, 635–648. 10.1063/1.1665178Search in Google Scholar

[15] V. Pivovarchik, Inverse problem for the Sturm–Liouville equation on a simple graph, SIAM J. Math. Anal. 32 (2000), no. 4, 801–819. 10.1137/S0036141000368247Search in Google Scholar

[16] J. Pöschel and E. Trubowitz, Inverse Spectral Theory, Pure Appl. Math. 130, Academic, Boston, 1987. Search in Google Scholar

[17] C.-T. Shieh and V. A. Yurko, Inverse nodal and inverse spectral problems for discontinuous boundary value problems, J. Math. Anal. Appl. 347 (2008), no. 1, 266–272. 10.1016/j.jmaa.2008.05.097Search in Google Scholar

[18] C.-F. Yang, An interior inverse problem for discontinuous boundary-value problems, Integral Equations Operator Theory 65 (2009), no. 4, 593–604. 10.1007/s00020-009-1693-ySearch in Google Scholar

[19] C.-F. Yang, Inverse spectral problems for the Sturm–Liouville operator on a d-star graph, J. Math. Anal. Appl. 365 (2010), no. 2, 742–749. 10.1016/j.jmaa.2009.12.016Search in Google Scholar

[20] C.-F. Yang, Inverse problems for the differential operator on a graph with cycles, J. Math. Anal. Appl. 445 (2017), no. 2, 1548–1562. 10.1016/j.jmaa.2016.01.007Search in Google Scholar

[21] C.-F. Yang and N. P. Bondarenko, A partial inverse problem for the Sturm–Liouville operator on the Lasso-graph, Inverse Probl. Imaging 13 (2019), no. 1, 69–79. 10.3934/ipi.2019004Search in Google Scholar

[22] C.-F. Yang and X.-P. Yang, An interior inverse problem for the Sturm–Liouville operator with discontinuous conditions, Appl. Math. Lett. 22 (2009), no. 9, 1315–1319. 10.1016/j.aml.2008.12.001Search in Google Scholar

[23] C.-F. Yang and X.-P. Yang, Uniqueness theorems from partial information of the potential on a graph, J. Inverse Ill-Posed Probl. 19 (2011), no. 4–5, 631–641. 10.1515/jiip.2011.059Search in Google Scholar

[24] V. Yurko, Integral transforms connected with discontinuous boundary value problems, Integral Transform. Spec. Funct. 10 (2000), no. 2, 141–164. 10.1080/10652460008819282Search in Google Scholar

[25] V. A. Yurko, On boundary value problems with discontinuity conditions inside an interval, Differ. Equ. 36 (2000), no. 8, 1266–1269. 10.1007/BF02754199Search in Google Scholar

[26] V. A. Yurko, Inverse problems for Sturm–Liouville operators on graphs with a cycle, Oper. Matrices 2 (2008), no. 4, 543–553. 10.7153/oam-02-34Search in Google Scholar

[27] V. A. Yurko, Inverse nodal problems for the Sturm–Liouville differential operators on a star-type graph, Sib. Math. J. 50 (2009), no. 2, 469–475. 10.1007/s11202-009-0043-2Search in Google Scholar

[28] V. A. Yurko, Inverse spectral problems for differential operators on spatial networks, Russian Math. Surveys 71 (2016), no. 3, 539–584. 10.1070/RM9709Search in Google Scholar

[29] R. Zhang, X.-C. Xu, C.-F. Yang and N. P. Bondarenko, Determination of the impulsive Sturm–Liouville operator from a set of eigenvalues, J. Inverse Ill-Posed Probl. 28 (2020), no. 3, 341–348. 10.1515/jiip-2019-0003Search in Google Scholar