Geodesic
Asymptotic behavior of generalized eigenvalues of the Schrödinger operator
Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 4, pp. 9-15 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The Schrödinger 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. 
@article{VMJ_2014_16_4_a1,
     author = {M. Sh. Badakhov and O. Y. Veremeenko and A. B. Shabat},
     title = {Asymptotic behavior of generalized eigenvalues of the {Schr\"odinger} operator},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {9--15},
     year = {2014},
     volume = {16},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2014_16_4_a1/}
}
TY  - JOUR
AU  - M. Sh. Badakhov
AU  - O. Y. Veremeenko
AU  - A. B. Shabat
TI  - Asymptotic behavior of generalized eigenvalues of the Schrödinger operator
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2014
SP  - 9
EP  - 15
VL  - 16
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VMJ_2014_16_4_a1/
LA  - ru
ID  - VMJ_2014_16_4_a1
ER  - 
%0 Journal Article
%A M. Sh. Badakhov
%A O. Y. Veremeenko
%A A. B. Shabat
%T Asymptotic behavior of generalized eigenvalues of the Schrödinger operator
%J Vladikavkazskij matematičeskij žurnal
%D 2014
%P 9-15
%V 16
%N 4
%U http://geodesic.mathdoc.fr/item/VMJ_2014_16_4_a1/
%G ru
%F VMJ_2014_16_4_a1
M. Sh. Badakhov; O. Y. Veremeenko; A. B. Shabat. Asymptotic behavior of generalized eigenvalues of the Schrödinger operator. Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 4, pp. 9-15. http://geodesic.mathdoc.fr/item/VMJ_2014_16_4_a1/

[1] Koosis P., The logariphmic integral, v. I, Cambridge, 1997

[2] Baker G., Graves-Morris P., Pade approximants, Enciclopedia of Math. and its Appl., 59, 2nd ed., CUP, Cambridge, 1996, 335–414 | MR

[3] Albeverio S., Khëeg-Kron R., Gestezi F., Reshaemye modeli v kvantovoi mekhanike, Mir, M., 1991, 569 pp. | MR

[4] Khabibullin I., Shabat A., Zadacha Shturma–Liuvillya, Bashgosuniver, Ufa, 1985

[5] Zakharov V., Shabat A., “Integrirovanie nelineinykh uravnenii matematicheskoi fiziki metodom obratnoi zadachi rasseyaniya, II”, Funkts. analiz i ego pril., 13:3 (1979), 13–22 | MR | Zbl

[6] Korotyaev Evg., “Inverse scattering on the real line”, Inverse Problems, 21 (2005), 325–341 | DOI | MR | Zbl

[7] Zhura N. A., Soldatov A. P., “K resheniyu obratnoi zadachi Shturma–Liuvillya na vsei osi”, Dokl. AN, 453:4 (2013), 368–372 | DOI | MR | Zbl

[8] Shabat A. B., “Obratnaya zadacha rasseyaniya dlya sistemy differentsialnykh uravnenii”, Funkts. analiz i ego pril., 9:3 (1975), 75–78 | MR | Zbl

[9] Shabat A. B., “Ob odnoi interpolyatsionnoi zadache”, Issledovaniya po dif. uravneniyam, mat. modelirovaniyu i problemam mat. obrazovaniya, Itogi nauki. Yug Rossii. Mat. forum, 8, ch. 2, YuMI VNTs RAN i RSO-A, Vladikavkaz, 2014, 66–74

[10] Shabat A. B., “Ratsionalnaya interpolyatsiya i solitony”, Teor. i mat. fizika, 179:3 (2014), 303–316 | DOI | MR | Zbl

[11] Povzner A. Ya., “O differentsialnykh uravneniyakh tipa Shturma–Liuvillya na poluosi”, Mat. sb., 23(65):1 (1948), 3–52 | MR | Zbl

[12] Agranovich Z. S., Marchenko V. A., Obratnaya zadacha rasseyaniya, Izd-vo Kharkovskogo un-ta, Kharkov, 1960, 268 pp.

[13] Marchenko V. A., Sturm–Liouville Operators and Applications, Birkhaüser Verlag, Basel, 1986 | MR | Zbl