Geodesic
The scattering problem for a discrete Sturm–Liouville operator
Sbornik. Mathematics, Tome 49 (1984) no. 2, pp. 325-355 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper properties of the discrete Sturm–Liouville operator are considered, and the scattering problem for this operator is studied using asymptotic formulas for orthogonal polynomials with matrix coefficients. Bibliography: 22 titles. 
@article{SM_1984_49_2_a3,
     author = {A. I. Aptekarev and E. M. Nikishin},
     title = {The scattering problem for a~discrete {Sturm{\textendash}Liouville} operator},
     journal = {Sbornik. Mathematics},
     pages = {325--355},
     year = {1984},
     volume = {49},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1984_49_2_a3/}
}
TY  - JOUR
AU  - A. I. Aptekarev
AU  - E. M. Nikishin
TI  - The scattering problem for a discrete Sturm–Liouville operator
JO  - Sbornik. Mathematics
PY  - 1984
SP  - 325
EP  - 355
VL  - 49
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1984_49_2_a3/
LA  - en
ID  - SM_1984_49_2_a3
ER  - 
%0 Journal Article
%A A. I. Aptekarev
%A E. M. Nikishin
%T The scattering problem for a discrete Sturm–Liouville operator
%J Sbornik. Mathematics
%D 1984
%P 325-355
%V 49
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1984_49_2_a3/
%G en
%F SM_1984_49_2_a3
A. I. Aptekarev; E. M. Nikishin. The scattering problem for a discrete Sturm–Liouville operator. Sbornik. Mathematics, Tome 49 (1984) no. 2, pp. 325-355. http://geodesic.mathdoc.fr/item/SM_1984_49_2_a3/

[1] Gelfand I. M., Levitan B. M., “Ob opredelenii differentsialnogo uravneniya po ego spektralnoi funktsii”, Izv. AN SSSR. Seriya matem., 15 (1951), 309–360 | MR | Zbl

[2] Agranovich 3. S., Marchenko V. A., Obratnaya zadacha teorii rasseyaniya, Izd-vo Khark. un-ta, 1960

[3] Faddeev L. D., “Svoistva $S$-matritsy odnomernogo uravneniya Shredingera”, Trudy matem. in-ta im. V. A. Steklova AN SSSR, 73 (1964), 314–336 | MR | Zbl

[4] Case K. M., Chiu S. C., “The discrete version of the Marchenko equations in the inverse scattering problem”, J. Math. Phys., 14:11 (1973), 1643–1647 | DOI | MR

[5] Guseinov G. Sh., “Opredelenie beskonechnoi matritsy Yakobi po dannym rasseyaniya”, DAN SSSR, 227:6 (1976), 1289–1292 | MR | Zbl

[6] Serebryakov V. P., “Obratnaya zadacha teorii rasseyaniya dlya raznostnykh uravnenii s matrichnymi koeffitsientami”, DAN SSSR, 250:3 (1980), 562–565 | MR | Zbl

[7] Nikishin E. M., “Diskretnyi operator Shturma–Liuvillya i nekotorye zadachi teorii funktsii”, Trudy seminara im. I. G. Petrovskogo, 8 (1983)

[8] Sekefalvi-Nad B., Foyash Ch., Garmonicheskii analiz operatorov v gilbertovom prostranstve, Mir, M., 1970 | MR

[9] Akhiezer N. I., Glazman I. M., Teoriya lineinykh operatorov v gilbertovom prostranstve, Nauka, M., 1966 | MR | Zbl

[10] Geronimus Ya. L., Mnogochleny, ortogonalnye na okruzhnosti i na otrezke, Fizmatgiz, M., 1958 | Zbl

[11] Markus A. S, Mink X., Obzor po teorii matrits i matrichnykh neravenstv, Nauka, M., 1972 | MR

[12] Potapov V. P., “Multiplikativnaya struktura $J$-nerastyagivayuschikh matrits”, Trudy MMO, 1955, no. 4, 25–236

[13] Kats I., “O gilbertovykh prostranstvakh, porozhdaemykh monotonnymi ermitovymi matritsami-funktsiyami”, Zapiski NII matem. i mekhan. i Khark. matem. ob-va, XXII (1950), 95–113

[14] Ginzburg Yu. P., “O faktorizatsii analiticheskikh matrits-funktsii”, DAN SSSR, 159:3 (1964), 484–493

[15] Privalov I. I., Granichnye svoistva analiticheskikh funktsii, GONTI, M., L., 1950

[16] Gonchar A. A., “O skhodimosti approksimatsii Pade dlya nekotorykh klassov meromorfnykh funktsii”, Matem. sb., 97 (139) (1975), 607–629 | Zbl

[17] Arov D. Z., Krein M. G., “Zadacha ob otyskanii minimuma entropii v neopredelennykh problemakh prodolzheniya”, Funkts. analiz, 15:2 (1981), 61–64 | MR | Zbl

[18] Atkinson F., Diskretnye i nepreryvnye granichnye zadachi, Mir, M., 1968 | MR | Zbl

[19] Faddeev L. D., “Obratnaya zadacha kvantovoi teorii rasseyaniya”, UMN, 14:4 (1959), 57–119 | MR

[20] Newton R. G., Iost R., “The construction of Potentials from the $S$-Matrix for Systems of Differentials Equations. II”, Nuovo Cimento, 1:4 (1955), 590–622 | DOI | MR | Zbl

[21] Shadan K., Sabate P., Obratnye zadachi v kvantovoi teorii rasseyaniya, Mir, M., 1980 | MR

[22] Delsarte P., Genin Y. V., Kamp Y. G., “Ortogonal Polinomial Matrices on the Unit Circle”, IEEE Trans. Circuits and Syst., 25:3 (1978), 149–160 | DOI | MR | Zbl