Journal of Samara State Technical University, Ser. Physical and Mathematical SciencesJournal of Samara State Technical University, Ser. Physical and Mathematical Sciences1991-86152310-7081Samara State Technical University2057910.14498/vsgtu1599Research ArticleOn an inverse Regge problem for the Sturm-Liouville operator with deviating argumentIgnatievMikhail YuCand. Phys. & Math. Sci.; Associate Professor; Dept. of Mathematical Physics and Computational MathematicsIgnatievMU@info.sgu.ruN. G. Chernyshevsky Saratov State University (National Research University)1506201822220321314022020Copyright © 2018, Samara State Technical University2018Boundary value problem of the formdifferential operatorsdeviating argumentconstant delayinverse spectral problemsRegge problemдифференциальные операторыотклоняющийся аргументпостоянное запаздываниеобратные спектральные задачизадача РеджеIntroduction. Consider the boundary value problem: -[Marchenko V. A. Sturm-Liouville operators and applications, Operator Theory: Advances and Applications, vol. 22. Basel, Boston, Stuttgart, Birkhäuser Verlag, 1986, xi+367 pp.; Russ. ed.: Kiev, Naukova Dumka, 1977, 393 pp.][Levitan B. M. Inverse Sturm-Liouville problems. Utrecht, VNU Science Press, 1987, x+240 pp.; Russ. ed.: Moscow, Nauka, 1984, 246 pp.][Beals R., Deift P., Tomei C. Direct and inverse scattering on the line, Mathematical Surveys and Monographs, vol. 28. Providence, RI, American Mathematical Society, 1988, xiii+209 pp.][Yurko V. A. Introduction to the theory of universe spectral problems. Moscow, Fizmatlit, 2007, 384 pp. (In Russian)][Buterin S. A. On an inverse spectral problem for a convolution integro-differential operator, Result. Math., 2007, vol. 50, no. 3-4, pp. 73-181. doi: 10.1007/s00025-007-0244-6.][Kuryshova Ju. V. Inverse spectral problem for integro-differential operators, Math. Notes, 2007, vol. 81, no. 6, pp. 767-777. doi: 10.1134/S0001434607050240.][Bondarenko N. P., Buterin S. A. On recovering the Dirac operator with an integral delay from the spectrum, Result. Math., 2017, vol. 71, no. 3, pp. 1521-1529. doi: 10.1007/s00025-016-0568-1.][Freiling G., Yurko V. A. Inverse problems for Sturm-Liouville differential operators with a constant delay, Appl. Math. Lett., 2012, vol. 25, no. 11, pp. 1999-2004. doi: 10.1016/j.aml.2012.03.026.][Vladičić V., Pikula M. An inverse problem for Sturm-Liouville-type differential equation with a constant delay, Sarajevo J. Math., 2016, vol. 12(24), no. 1, pp. 83-88. doi: 10.5644/SJM.12.1.06.][Buterin S. A., Pikula M., Yurko V. A. Sturm-Liouville differential operators with deviating argument, Tamkang J. Math., 2017, vol. 48, no. 1, pp. 61-71. doi: 10.5556/j.tkjm.48.2017.2264.][Yurko V. A., Buterin S. A. An inverse spectral problem for Sturm-Liouville operators with a large constant delay, Anal. Math. Phys., 2017. doi: 10.1007/s13324-017-0176-6.][Gubreev G. M., Pivovarchik V. N. Spectral analysis of the Regge problem with parameters, Funct. Anal. Appl., 1997, vol. 31, no. 1, pp. 54-57. doi: 10.1007/BF02466004.][Levin B. Ya. Distribution of zeros of entire functions, Translations of Mathematical Monographs, Providence, R.I., 1964, viii+493 pp.; Russ. ed.: Moscow, Gostechizdat, 1956, 632 pp.][Sedletskiy A. M. Classes of analytic Fourier transforms and exponential approximations. Moscow, Fizmatlit, 2005, 504 pp. (In Russian)][Gesztesy F., Simon B. Inverse spectral analysis with partial information on the potential, II. The case of discrete spectrum, Trans. Amer. Math. Soc., 2000, vol. 352, no. 6, pp. 2765-2787. doi: 10.1090/S0002-9947-99-02544-1.]