Geodesic
Direct and inverse problems for an operator with nonlocal potential
Sbornik. Mathematics, Tome 203 (2012) no. 12, pp. 1785-1807 Cet article a éte moissonné depuis la source Math-Net.Ru

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The spectrum of a selfadjoint operator which is a one-dimensional perturbation of the second derivative operator on a finite interval is analysed. It is shown that all the components of the one-dimensional perturbation can be recovered from two spectra up to complex conjugation. Bibliography: 13 titles.
Keywords: inverse spectral problem, one-dimensional perturbation of the second derivative operator. 
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V. A. Zolotarev. Direct and inverse problems for an operator with nonlocal potential. Sbornik. Mathematics, Tome 203 (2012) no. 12, pp. 1785-1807. http://geodesic.mathdoc.fr/item/SM_2012_203_12_a5/

[1] B. M. Levitan, I. S. Sargsjan, Introduction to spectral theory: selfadjoint ordinary differential operators, Translations of Mathematical Monographs, 39, Amer. Math. Soc., Providence, RI, 1975 | MR | MR | Zbl | Zbl

[2] B. M. Levitan, Inverse Sturm–Liouville problems, VNU Science Press, Utrecht, 1987 | MR | MR | Zbl | Zbl

[3] E. C. Titchmarsh, Eigenfunction expansions associated with second-order differential equations, v. I, Clarendon Press, Oxford, 1946 | MR | MR | Zbl | Zbl

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

[5] K. Chadan, P. C. Sabatier, Inverse problems in quantum scattering theory, Springer-Verlag, New York–Berlin, 1977 | MR | MR | Zbl

[6] V. Heine, M. L. Cohen, D. Weaire, Solid state physics, Academic Press, New York, 1970

[7] B. Ya. Levin, Lectures on entire functions, Transl. Math. Monogr., 150, Amer. Math. Soc., Providence, RI, 1996 | MR | Zbl

[8] E. C. Titchmarsh, Introduction to the theory of Fourier integrals, Clarendon Press, Oxford, 1937 | Zbl

[9] N. I. Akhiezer, Lectures on integral transforms, Transl. Math. Monogr., 70, Amer. Math. Soc., Providence, RI, 1988 | MR | MR | Zbl | Zbl

[10] M. A. Lavrentev, B. V. Shabat, Metody teorii funktsii kompleksnogo peremennogo, Nauka, M., 1973 | MR | Zbl

[11] B. V. Shabat, Introduction à l'analyse complexe, Mir, Moscow, 1990 | MR | MR | MR | Zbl | Zbl

[12] H. M. Nussenzveig, Causality and dispersion relations, Academic Press, Hardcover, 1970

[13] F. D. Gakhov, Boundary value problems, Pergamon, London–Paris–Frankfurt; Addison-Wesley, Reading, MA, 1966 | MR | MR | Zbl | Zbl