Local solvability and stability of the generalized inverse Robin–Regge problem with complex coefficients

References

[1] T. Aktosun, A. Machuca and P. Sacks, Determining the shape of a human vocal tract from pressure measurements at the lips, Inverse Problems 33 (2017), no. 11, Paper No. 115002. 10.1088/1361-6420/aa882dSuche in Google Scholar

[2] N. P. Bondarenko, Inverse Sturm–Liouville problem with analytical functions in the boundary condition, Open Math. 18 (2020), no. 1, 512–528. 10.1515/math-2020-0188Suche in Google Scholar

[3] N. P. Bondarenko, Local solvability and stability of the inverse problem for the non-self-adjoint Sturm–Liouville operator, Bound. Value Probl. 2020 (2020), Paper No. 123. 10.1186/s13661-020-01422-4Suche in Google Scholar

[4] N. P. Bondarenko, Solvability and stability of the inverse Sturm–Liouville problem with analytical functions in the boundary condition, Math. Methods Appl. Sci. 43 (2020), no. 11, 7009–7021. 10.1002/mma.6451Suche in Google Scholar

[5] G. Borg, Eine Umkehrung der Sturm–Liouvilleschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte, Acta Math. 78 (1946), 1–96. 10.1007/BF02421600Suche in Google Scholar

[6] S. Buterin and M. Kuznetsova, On Borg’s method for non-selfadjoint Sturm–Liouville operators, Anal. Math. Phys. 9 (2019), no. 4, 2133–2150. 10.1007/s13324-019-00307-9Suche in Google Scholar

[7] S. A. Buterin, On inverse spectral problem for non-selfadjoint Sturm–Liouville operator on a finite interval, J. Math. Anal. Appl. 335 (2007), no. 1, 739–749. 10.1016/j.jmaa.2007.02.012Suche in Google Scholar

[8] S. A. Buterin, A. E. Choque-Rivero and M. A. Kuznetsova, On a regularization approach to the inverse transmission eigenvalue problem, Inverse Problems 36 (2020), no. 10, Paper No. 105002. 10.1088/1361-6420/abaf3cSuche in Google Scholar

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

[10] V. V. Kravchenko and S. M. Torba, A practical method for recovering Sturm–Liouville problems from the Weyl function, Inverse Problems 37 (2021), no. 6, Paper No. 065011. 10.1088/1361-6420/abff06Suche in Google Scholar

[11] M. G. Kreĭn and A. A. Nudelman, Direct and inverse problems for the frequencies of boundary dissipation of a nonuniform string, Dokl. Akad. Nauk SSSR 247 (1979), no. 5, 1046–1049. Suche in Google Scholar

[12] M. G. Kreĭn and A. A. Nudelman, Some spectral properties of a nonhomogeneous string with a dissipative boundary condition, J. Operator Theory 22 (1989), no. 2, 369–395. Suche in Google Scholar

[13] B. M. Levitan, Inverse Sturm–Liouville Problems, “Nauka”, Moscow, 1987. 10.1515/9783110941937Suche in Google Scholar

[14] V. A. Marchenko, Sturm–Liouville Operators and Applications, Oper. Theory Adv. Appl. 22, Birkhäuser, Basel, 1986. 10.1007/978-3-0348-5485-6Suche in Google Scholar

[15] M. Marletta and R. Weikard, Weak stability for an inverse Sturm–Liouville problem with finite spectral data and complex potential, Inverse Problems 21 (2005), no. 4, 1275–1290. 10.1088/0266-5611/21/4/005Suche in Google Scholar

[16] M. Möller and V. Pivovarchik, Spectral Theory of Operator Pencils, Hermite–Biehler Functions, and Their Applications, Oper. Theory Adv. Appl. 246, Birkhäuser/Springer, Cham, 2015. 10.1007/978-3-319-17070-1Suche in Google Scholar

[17] M. Möller and V. Pivovarchik, Direct and inverse Robin–Regge problems, Electron. J. Differential Equations 2017 (2017), Paper No. 287. Suche in Google Scholar

[18] V. Pivovarchik and C. van der Mee, The inverse generalized Regge problem, Inverse Problems 17 (2001), no. 6, 1831–1845. 10.1088/0266-5611/17/6/318Suche in Google Scholar

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

[20] T. Regge, Construction of potentials from resonance parameters, Nuovo Cimento 9 (1958), 491–503. 10.1007/BF02725104Suche in Google Scholar

[21] W. Rundell and P. Sacks, Numerical technique for the inverse resonance problem, J. Comput. Appl. Math. 170 (2004), no. 2, 337–347. 10.1016/j.cam.2004.01.035Suche in Google Scholar

[22] W. Rundell and P. E. Sacks, Reconstruction techniques for classical inverse Sturm–Liouville problems, Math. Comp. 58 (1992), no. 197, 161–183. 10.1090/S0025-5718-1992-1106979-0Suche in Google Scholar

[23] B. Simon, Resonances in one dimension and Fredholm determinants, J. Funct. Anal. 178 (2000), no. 2, 396–420. 10.1006/jfan.2000.3669Suche in Google Scholar

[24] X.-C. Xu, Inverse spectral problems for the generalized Robin–Regge problem with complex coefficients, J. Geom. Phys. 159 (2021), Paper No. 103936. 10.1016/j.geomphys.2020.103936Suche in Google Scholar

[25] X.-C. Xu and N. P. Bondarenko, On the local solvability and stability for the inverse spectral problem of the generalized Dirichlet-Regge problem, Acta Math. Sin. (Engl. Ser.) 38 (2022), no. 7, 1229–1240. 10.1007/s10114-022-1103-9Suche in Google Scholar

[26] V. A. Yurko, Boundary value problems with a parameter in the boundary conditions, Sov. J. Contemp. Math. Anal. 19 (1984), 62–73. Suche in Google Scholar