Asymptotic behavior of generalized eigenvalues of the schrodinger operator

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Home Editorial board Publication ethics Peer review guidelines Latest issue All issues Rules for authors Online submission system's guidelines Submit manuscript Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 E-mail: rio@smath.ru	DOI: 10.23671/VNC.2014.4.10253 Asymptotic behavior of generalized eigenvalues of the schrodinger operator Badakhov M. Sh. , Veremeenko O. Y. , Shabat A. B. Vladikavkaz Mathematical Journal 2014. Vol. 16. Issue 4. Abstract: The Schrodinger operator on the real line with compactly supported potential is considered. An asymptotic analysis of complex poles of the transmission coefficient \(1/a(k)\) for some \(\delta\)-type potentials is fulfilled. We are planning to use these poles producing effective methods of approximate solutions of the inverse scattering problem in the one-dimensional case. Keywords: inverse scattering problem, zeros of entire functions Language: Russian Download the full text For citation: Badakhov M. Sh., Veremeenko O. Y., Shabat A. B. Asymptotic behavior of generalized eigenvalues of the schrodinger operator // Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 16, no. 4, pp. 9-15. DOI 10.23671/VNC.2014.4.10253 + References 1. Koosis P. The Logariphmic Integral, I, Cambridge, 1997. 2. Baker G., Graves-Morris P. Pade approximants, 2nd ed. Enciclopedia of Math. and its Appl., Cambridge, CUP, 1996, vol. 59, pp. 335-414. 3. Albeverio S., Hoegh-Krohn R., Gesztesy F. Reshaemye Modeli v Kvantovoj Mehanike [Solvable Models in Quantum Mechanics], Moskva, Mir, 1991, 569 p. (Russian). 4. Habibullin I., Shabat A. Zadacha Shturma - Liuvillja, Ufa, Bashgosuniver, 1985 (Russian). 5. Zakharov V. E., Shabat A. B. Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II. Funct. Anal. Appl., 1979, vol. 13, no. 3, pp. 166-174. 6. Korotyaev E. Inverse scattering on the real line. Inverse Problems, 2005, vol. 21, pp. 325-341. 7. Zhura N. A., Soldatov A. P. To the solution of the inverse Sturm-Liouville problem on the real axis. Doklady Mathematics, 2013, vol. 88, no. 3, pp. 695-699. 8. Shabat A. B. Inverse-scattering problem for a system of differential equations. Funct. Anal. Appl., 1975, vol. 9, no. 3, pp. 244-247. 9. Shabat A. B. On an interpolation problem. Mat. Forum. Vol. 8, Ch. 2. Issledovanija po Dif. Uravnenijam, Mat. Modelirovaniju i Problemam Mat. Obrazovanija [Math. Forum. Vol. 8, part 2. Studies on Dif. Equations, Math. Modeling, and Problems in Math. Education], Vladikavkaz, UMI VNC RAN I RSO-A, 2014, pp. 66-74 (Russian). 10. Shabat A. B. Rational interpolation and solitons. Theoretical and Mathematical Physics, 2014, vol. 179, no. 3, pp. 637-648. 11. Povzner A. On differential equations of Sturm-Liouville type on a half-axis. Mat. Sb. (N.S.) [Math. Sb.], 1948, vol. 23(65), no. 1, pp. 3-52 (Russian). 12. Agranovich Z. S., Marchenko V. A. Obratnaja Zadacha Rassejanija, Har'kov, Izd-vo Har'kovskogo Un-ta, 1960, 268 p. (Russian). 13. Marchenko V. A. Sturm-Liouville Operators and Applications, Basel, Birkhauser Verlag, 1986. The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses. ← Contents of issue


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