Geodesic
Reconstruction of potential of discontinuous Sturm — Liouville operator from spectral data
Ufa mathematical journal, Tome 16 (2024) no. 4, pp. 116-123 Cet article a éte moissonné depuis la source Math-Net.Ru

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We deal with the inverse spectral problem of the discontinuous Sturm — Liouville operator. The aim is we to determine the potential $q(x)$ and the boundary constant $h$ by a given spectral data. We provide the algorithm for reconstructing the potential $q(x)$ from the spectral data.
Keywords: discontinuous Sturm — Liouville operator, inverse problem, spectral data. 
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O. Akcay. Reconstruction of potential of discontinuous Sturm — Liouville operator from spectral data. Ufa mathematical journal, Tome 16 (2024) no. 4, pp. 116-123. http://geodesic.mathdoc.fr/item/UFA_2024_16_4_a8/

[1] O. Akcay, “The representation of the solution of Sturm — Liouville equation with discontinuity conditions”, Acta Math. Sci., Ser. B, Engl. Ed., 38:4 (2018), 1195–1213 | DOI | MR | Zbl

[2] B.P. Allahverdiev, E. Bairamov, E. Ugurlu, “Eigenparameter dependent Sturm — Liouville problems in boundary conditions with transmission conditions”, J. Math. Anal. Appl., 401:1 (2013), 388–396 | DOI | MR | Zbl

[3] I.M. Guseinov, L.I. Mammadova, “Reconstruction of the diffusion equation with singular coefficients for two spectra”, Dokl. Math., 90:1 (2014), 401–404 | DOI | MR | Zbl

[4] O.Sh. Mukhtarov, H. Olğar, K. Aydemir, I.Sh. Jabbarov, “Operator-pencil realization of one Sturm — Liouville problem with transmission conditions”, Appl. Comput. Math., 17:3 (2018), 284–294 | MR | Zbl

[5] Y.P. Wang, V.A. Yurko, “On the inverse nodal problems for discontinuous Sturm — Liouville operators”, J. Differ. Equations, 260:5 (2016), 4086–4109 | DOI | MR | Zbl

[6] C.F. Yang, “Inverse problems for the Sturm — Liouville operator with discontinuity”, Inverse Probl. Sci. Eng., 22:2 (2014), 232–244 | DOI | MR | Zbl

[7] E.N. Akhmedova, H.M. Huseynov, “On inverse problem for Sturm — Liouville operator with discontinuous coefficients”, Izv. Saratov Univ. Math. Mech. Informatics, 10:1 (2010), 3–9

[8] D. Karahan, Kh.R. Mamedov, I.F. Hashimoglu, “On main equation for inverse Sturm — Liouville operator with discontinuous coefficient”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 225, 2023, 73–86 | MR

[9] Ufa Math. J., 7:3 (2015), 119–131 | DOI | MR

[10] A.A. Nabiev, M. Gürdal, S. Saltan, “Inverse problems for the Sturm — Liouville equation with the discontinuous coefficient”, J. Appl. Anal. Comput., 7:2 (2017), 559–580 | MR | Zbl

[11] O. Akcay, “On the boundary value problem for discontinuous Sturm — Liouville operator”, Mediterr. J. Math., 16:1 (2019), 7 | DOI | MR | Zbl

[12] O.A. Karakus, “On determination of discontinuous Sturm — Liouville operator from Weyl function”, Malaya J. Mat., 11:4 (2023), 356–362 | DOI | MR

[13] O. Akcay, “Uniqueness theorems for inverse problems of discontinuous Sturm — Liouville operator”, Bull. Malays. Math. Sci. Soc. (2), 44:4 (2021), 1927–1940 | DOI | MR | Zbl

[14] G. Freiling, V.A. Yurko, Inverse Sturm — Liouville problems and their applications, Nova Science Publishers Inc., Huntington, NY, 2001 | MR | Zbl

[15] T. Aktosun, M. Klaus, C. van der Mee, “Recovery of discontinuities in a non–homogeneous medium”, Inverse Probl., 12:1 (1996), 1–25 | DOI | MR | Zbl

[16] O.H. Hald, “Discontinuous inverse eigenvalue problems”, Commun. Pure Appl. Math., 37 (1984), 539–577 | DOI | MR | Zbl

[17] R.J. Krueger, “Inverse problems for nonabsorbing media with discontinuous material properties”, J. Math. Phys., 23:3 (1982), 396–404 | DOI | MR | Zbl

[18] V.P. Meschanov, A.L. Feldstein, Automatic design of microwave directional couplers, Sviaz, M., 1980 (in Russian)

[19] D.G. Shepelsky, “The inverse problem of reconstruction of the medium's conductivity in a class of discontinuous and increasing functions”, Spectral operator theory and related topics, Collection of papers, Adv. Sov. Math., 19, American Mathematical Society, Providence, RI, 1994, 209–232 | MR | Zbl

[20] A. Gomilko, V. Pivovarchik, “On basis properties of a part of eigenfunctions of the problem of vibrations of a smooth inhomogeneous string damped at the midpoint”, Math. Nachr., 245:1 (2002), 72–93 | 3.0.CO;2-X class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl