Method for solving inverse spectral problems on quantum star graphs

References

[1] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1972. Search in Google Scholar

[2] M. Arioli and M. Benzi, A finite element method for quantum graphs, IMA J. Numer. Anal. 38 (2018), no. 3, 1119–1163. 10.1093/imanum/drx029Search in Google Scholar

[3] S. A. Avdonin, B. P. Belinskiy and J. V. Matthews, Inverse problem on the semi-axis: Local approach, Tamkang J. Math. 42 (2011), no. 3, 275–293. 10.5556/j.tkjm.42.2011.916Search in Google Scholar

[4] S. A. Avdonin and J. Bell, Determining a distributed conductance parameter for a neuronal cable model defined on a tree graph, Inverse Probl. Imaging 9 (2015), no. 3, 645–659. 10.3934/ipi.2015.9.645Search in Google Scholar

[5] S. A. Avdonin, A. Choque Rivero, G. Leugering and V. Mikhaylov, On the inverse problem of the two velocity tree-like graph, Z. Angew. Math. Mech. 95 (2015), no. 12, 1490–1500. 10.1002/zamm.201400126Search in Google Scholar

[6] S. A. Avdonin and P. Kurasov, Inverse problems for quantum trees, Inverse Probl. Imaging 2 (2008), no. 1, 1–21. 10.3934/ipi.2008.2.1Search in Google Scholar

[7] S. A. Avdonin, G. Leugering and V. Mikhaylov, On an inverse problem for tree-like networks of elastic strings, Z. Angew. Math. Mech. 90 (2010), no. 2, 136–150. 10.1002/zamm.200900295Search in Google Scholar

[8] M. I. Belishev and A. F. Vakulenko, Inverse problems on graphs: Recovering the tree of strings by the BC-method, J. Inverse Ill-Posed Probl. 14 (2006), no. 1, 29–46. 10.1515/156939406776237474Search in Google Scholar

[9] G. Berkolaiko and P. Kuchment, Introduction to Quantum Graphs, Math. Surveys Monogr. 186, American Mathematical Society, Providence, 2013. 10.1090/surv/186Search in Google Scholar

[10] B. M. Brown, V. S. Samko, I. W. Knowles and M. Marletta, Inverse spectral problem for the Sturm–Liouville equation, Inverse Problems 19 (2003), no. 1, 235–252. 10.1088/0266-5611/19/1/314Search in Google Scholar

[11] K. Chadan, D. Colton, L. Päivärinta and W. Rundell, An Introduction to Inverse Scattering and Inverse Spectral Problems, Society for Industrial and Applied Mathematics, Philadelphia, 1997. 10.1137/1.9780898719710Search in Google Scholar

[12] V. V. Kravchenko, On a method for solving the inverse Sturm–Liouville problem, J. Inverse Ill-Posed Probl. 27 (2019), no. 3, 401–407. 10.1515/jiip-2018-0045Search in Google Scholar

[13] V. V. Kravchenko, Direct and Inverse Sturm–Liouville Problems—A Method of Solution, Front. Math., Birkhäuser/Springer, Cham, 2020. 10.1007/978-3-030-47849-0Search in Google Scholar

[14] V. V. Kravchenko, L. J. Navarro and S. M. Torba, Representation of solutions to the one-dimensional Schrödinger equation in terms of Neumann series of Bessel functions, Appl. Math. Comput. 314 (2017), 173–192. 10.1016/j.amc.2017.07.006Search in Google Scholar

[15] V. V. Kravchenko and S. M. Torba, Analytic approximation of transmutation operators and applications to highly accurate solution of spectral problems, J. Comput. Appl. Math. 275 (2015), 1–26. 10.1016/j.cam.2014.07.022Search in Google Scholar

[16] V. V. Kravchenko and S. M. Torba, A direct method for solving inverse Sturm–Liouville problems, Inverse Problems 37 (2021), no. 1, Paper No. 015015. 10.1088/1361-6420/abce9fSearch in Google Scholar

[17] P. Kurasov, Quantum Graphs: Spectral Theory and Inverse Problems, to appear. Search in Google Scholar

[18] P. Kurasov and M. Nowaczyk, Inverse spectral problem for quantum graphs, J. Phys. A 38 (2005), no. 22, 4901–4915. 10.1088/0305-4470/38/22/014Search in Google Scholar

[19] J. E. Lagnese, G. Leugering and E. J. P. G. Schmidt, Modeling, Analysis and Control of Dynamic Elastic Multi-Link Structures, Systems Control Found. Appl., Birkhäuser, Boston, 1994. 10.1007/978-1-4612-0273-8Search in Google Scholar

[20] B. M. Levitan, Inverse Sturm–Liouville Problems, VSP, Zeist, 1987. 10.1515/9783110941937Search in Google Scholar

[21] D. Mugnolo, Semigroup Methods for Evolution Equations on Networks, Underst. Complex Syst., Springer, Cham, 2014. 10.1007/978-3-319-04621-1Search in Google Scholar

[22] A. M. Savchuk and A. A. Shkalikov, Inverse problem for Sturm–Liouville operators with distribution potentials: Reconstruction from two spectra, Russ. J. Math. Phys. 12 (2005), no. 4, 507–514. Search in Google Scholar

[23] E. Shishkina and S. Sitnik, Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics, Math. Sci. Eng., Elsevier/Academic, London, 2020. 10.1016/B978-0-12-819781-3.00017-3Search in Google Scholar

[24] V. Yurko, Inverse spectral problems for Sturm–Liouville operators on graphs, Inverse Problems 21 (2005), no. 3, 1075–1086. 10.1088/0266-5611/21/3/017Search in Google Scholar

[25] V. A. Yurko, Introduction to the Theory of Inverse Spectral Problems (in Russian), Fizmatlit, Moscow, 2007. Search in Google Scholar