On an inverse Regge problem for the Sturm-Liouville operator with deviating argument


Boundary value problem of the form

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Introduction. Consider the boundary value problem: -

About the authors

Mikhail Yu Ignatiev

N. G. Chernyshevsky Saratov State University (National Research University)

Email: IgnatievMU@info.sgu.ru
83, Astrakhanskaya st., Saratov, 410012, Russian Federation
Cand. Phys. & Math. Sci.; Associate Professor; Dept. of Mathematical Physics and Computational Mathematics


  1. 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.
  2. Levitan B. M. Inverse Sturm-Liouville problems. Utrecht, VNU Science Press, 1987, x+240 pp.; Russ. ed.: Moscow, Nauka, 1984, 246 pp.
  3. 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.
  4. Yurko V. A. Introduction to the theory of universe spectral problems. Moscow, Fizmatlit, 2007, 384 pp. (In Russian)
  5. 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.
  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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. Sedletskiy A. M. Classes of analytic Fourier transforms and exponential approximations. Moscow, Fizmatlit, 2005, 504 pp. (In Russian)
  15. 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.



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