Geodesic
On the Inverse Problem for Differential Operators on a Finite Interval with Complex Weights
Matematičeskie zametki, Tome 105 (2019) no. 2, pp. 313-320 Cet article a éte moissonné depuis la source Math-Net.Ru

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Inverse problems of spectral analysis for second-order differential operators on a finite interval with complex-valued weights and with an arbitrary number of discontinuity conditions for the solutions inside the interval are studied. Properties of the spectral characteristics are established, and uniqueness theorems for this class of inverse problems are proved.
Keywords: Sturm–Liouville operators, complex weights, inverse spectral problems. 
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V. A. Yurko. On the Inverse Problem for Differential Operators on a Finite Interval with Complex Weights. Matematičeskie zametki, Tome 105 (2019) no. 2, pp. 313-320. http://geodesic.mathdoc.fr/item/MZM_2019_105_2_a11/

[1] V. A. Marchenko, Operatory Shturma–Liuvillya i ikh prilozheniya, Naukova dumka, Kiev, 1977 | MR | Zbl

[2] B. M. Levitan, Obratnye zadachi Shturma–Liuvillya, Nauka, M., 1984 | MR

[3] G. Freiling, V. A. Yurko, Inverse Sturm–Liouville Problems and Their Applications, NOVA Sci. Publ., New York, 2001 | MR | Zbl

[4] V. A. Yurko, Method of Spectral Mappings in the Inverse Problem Theory, VSP, Utrecht, 2002 | MR | Zbl

[5] V. A. Yurko, Vvedenie v teoriyu obratnykh spektralnykh zadach, Fizmatlit, M., 2007

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

[7] R. S. Anderssen, “The effect of discontinuities in density and shear velocity on the asymptotic overtone structure of tortional eigenfrequencies of the Earth.”, Geophys. J. Int., 50:2 (1977), 303–309 | DOI

[8] O. H. Hald, “Discontinuous inverse eigenvalue problems”, Comm. Pure Appl. Math., 37:5 (1984), 539–577 | DOI | MR | Zbl

[9] V. A. Yurko, “O kraevykh zadachakh s usloviyami razryva vnutri intervala”, Differents. uravneniya, 36:8 (2000), 1139–1140 | MR | Zbl

[10] V. A. Yurko, “Integral transforms connected with discontinuous boundary value problems”, Integral Transform. Spec. Funct., 10:2 (2000), 141–164 | DOI | MR | Zbl

[11] L.-E. Andersson, “Inverse EV problems with discontinuous coefficients”, Inverse Problems, 4:2 (1988), 353–397 | DOI | MR | Zbl

[12] C. Coleman, J. McLaughlin, “Solution of the inverse spectral problem for an impedance with integrable derivative, I, II”, Comm. Pure Appl. Math., 46:2 (1993), 145–184 | DOI | MR | Zbl

[13] G. Freilng, V. Yurko, “Inverse problems for differential equations with turning points”, Inverse Problems, 13:5 (1997), 1247–1263 | DOI | MR

[14] G. Freilng, V. Yurko, “Inverse spectral problems for differential equations on the half-line with turning points”, J. Differential Equations, 154:2 (1999), 419–453 | DOI | MR

[15] V. A. Yurko, “Obratnaya zadacha dlya puchkov differentsialnykh operatorov na poluosi s tochkami povorota”, Fundament. i prikl. matem., 12:5 (2006), 237–246 | MR | Zbl

[16] M. A. Naimark, Lineinye differentsialnye operatory, Nauka, M., 1969 | MR | Zbl