Geodesic
Factorization of a~scattering matrix and the serial structure of its roots
Izvestiya. Mathematics , Tome 7 (1973) no. 1, pp. 215-245.

Voir la notice de l'article provenant de la source Math-Net.Ru

The singular inner factor of the scattering matrix of a system of ordinary differential equations is computed directly in explicit form in terms of the equation coefficients. It is shown that the set of complex roots of the scattering matrix has a serial structure that is matched with the structure of its singular factor. 
@article{IM2_1973_7_1_a9,
     author = {B. S. Pavlov},
     title = {Factorization of a~scattering matrix and the serial structure of its roots},
     journal = {Izvestiya. Mathematics },
     pages = {215--245},
     publisher = {mathdoc},
     volume = {7},
     number = {1},
     year = {1973},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1973_7_1_a9/}
}
TY  - JOUR
AU  - B. S. Pavlov
TI  - Factorization of a~scattering matrix and the serial structure of its roots
JO  - Izvestiya. Mathematics 
PY  - 1973
SP  - 215
EP  - 245
VL  - 7
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1973_7_1_a9/
LA  - en
ID  - IM2_1973_7_1_a9
ER  - 
%0 Journal Article
%A B. S. Pavlov
%T Factorization of a~scattering matrix and the serial structure of its roots
%J Izvestiya. Mathematics 
%D 1973
%P 215-245
%V 7
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1973_7_1_a9/
%G en
%F IM2_1973_7_1_a9
B. S. Pavlov. Factorization of a~scattering matrix and the serial structure of its roots. Izvestiya. Mathematics , Tome 7 (1973) no. 1, pp. 215-245. http://geodesic.mathdoc.fr/item/IM2_1973_7_1_a9/

[1] Pavlov B. S., “Teoriya rasseyaniya i “nefizicheskii list” dlya sistemy obyknovennykh differentsialnykh uravnenii”, Dokl. AN SSSR, 193:1 (1970), 36–39 | Zbl

[2] Laks P., Fillips R., Teoriya rasseyaniya, Mir, M., 1971 | MR

[3] Pavlov B. S., “O polnote nabora rezonansnykh sostoyanii dlya sistemy differentsialnykh uravnenii”, Dokl. AN SSSR, 196:1 (1971), 1272–1275 | MR | Zbl

[4] Buslaeva M. V., Teorema razlozheniya dlya translyatsionno invariantnykh podprostranstv nekotorykh obyknovennykh differentsialnykh operatorov, Kandidatskaya dissertatsiya, LGU, Leningrad, 1971 | MR

[5] Potapov V. P., “Multiplikativnaya struktura analiticheskikh $J$-nerastyagivayuschikh matrits-funktsii”, Tr. Mosk. matem. ob-va, 4, 1955, 125–236 | MR | Zbl

[6] Pavlov B. S., “O sovmestnoi polnote sistemy sobstvennykh funktsii szhatiya i ego sopryazhennogo”, Problemy matematicheskoi fiziki, no. 5, LGU, 1971, 101–112 | MR

[7] Nelson H., Lectures on invariant subspaces, N.Y., London, 1964

[8] Sigal E. I., “Faktor-kratnost kharakteristicheskogo chisla meromorfnoi operator-funktsii”, Matematicheskie issledovaniya, 5:4 (1970), 136–152 | MR | Zbl

[9] Sigal E. I., “O kratnosti kharakteristicheskogo chisla proizvedeniya operator-funktsii”, Matematicheskie issledovaniya, 5:1 (1970), 118–127 | MR | Zbl

[10] Eni V. M., “Ob ustoichivosti kornevogo chisla analiticheskoi operator-funktsii i o vozmuscheniyakh ee kharakteristicheskikh chisel i sobstvennykh vektorov”, Dokl. AN SSSR, 176:6 (1967), 1251–1254 | MR

[11] Gokhberg I. Ts., Sigal E. I., “Operatornoe obobschenie teoremy o logarifmicheskom vychete i teoremy Rushe”, Matem. sb., 84:4 (1971), 607–629 | Zbl

[12] Pavlov B. S., “O differentsialnom operatore s razmazannym granichnym usloviem”, Problemy matematicheskoi fiziki, no. 6, LGU, 1972, 101–118

[13] Nikolskii N. K., Pavlov B. S., “Bazisy iz sobstvennykh vektorov vpolne neunitarnykh szhatii i kharakteristicheskaya funktsiya”, Izv. AN SSSR. Ser. matem., 34 (1970), 90–133 | MR

[14] Marchenko V. A., Obratnaya zadacha teorii rasseyaniya, Kharkovsk. un-t, Kharkov, 1960 | Zbl