Geodesic
On a method in scattering theory
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 72 (2011) no. 2, pp. 189-205.

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

We use the well-studied Friedrichs model to showcase a new method for proving the asymptotic completeness of two operators, which in our case are the Friedrichs operator $A$ and the operator obtained from $A$ by omitting the integral term. Technically, the problem is reduced to a detailed analysis of the Fredholm determinant and minor of an auxiliary integral operator. 
@article{MMO_2011_72_2_a0,
     author = {E. R. Akchurin and R. A. Minlos},
     title = {On a method in scattering theory},
     journal = {Trudy Moskovskogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {189--205},
     publisher = {mathdoc},
     volume = {72},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MMO_2011_72_2_a0/}
}
TY  - JOUR
AU  - E. R. Akchurin
AU  - R. A. Minlos
TI  - On a method in scattering theory
JO  - Trudy Moskovskogo matematičeskogo obŝestva
PY  - 2011
SP  - 189
EP  - 205
VL  - 72
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MMO_2011_72_2_a0/
LA  - ru
ID  - MMO_2011_72_2_a0
ER  - 
%0 Journal Article
%A E. R. Akchurin
%A R. A. Minlos
%T On a method in scattering theory
%J Trudy Moskovskogo matematičeskogo obŝestva
%D 2011
%P 189-205
%V 72
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MMO_2011_72_2_a0/
%G ru
%F MMO_2011_72_2_a0
E. R. Akchurin; R. A. Minlos. On a method in scattering theory. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 72 (2011) no. 2, pp. 189-205. http://geodesic.mathdoc.fr/item/MMO_2011_72_2_a0/

[1] Akchurin E. R., Minlos R. A., “Ob odnom novom prieme v teorii rasseyaniya”, Vestnik MGU, 2010, no. 6, 27–32

[2] Faddeev L. D., “O modeli Fridrikhsa v teorii vozmuschenii nepreryvnogo spektra”, Trudy matem. in-ta AN SSSR, 73 (1964), 292–313 | MR | Zbl

[3] Yafaev D. R., Matematicheskaya teoriya rasseyaniya. Obschaya teoriya, Izd-vo LGU, L., 1994

[4] Gelfand I. M., Shilov G. E., Obobschennye funktsii, v. I, Obobschennye funktsii i deistviya nad nimi, Gostekhizdat, M., 1959

[5] Gelfand I. M., Shilov G. E., Obobschennye funktsii, v. II, Prostranstva osnovnykh i obobschennykh funktsii, Gostekhizdat, M., 1958

[6] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, v. 3, Mir, M., 1982

[7] Riss F., Sëkefalvi-Nad B., Lektsii po funktsionalnomu analizu, Mir, M., 1979

[8] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1972

[9] Lovitt U. V., Lineinye integralnye uravneniya, Gostekhizdat, M., 1957

[10] Muskhelishvili N. I., Singulyarnye integralnye uravneniya, Nauka, M., 1968

[11] Privalov I. I., Granichnye svoistva analiticheskikh funktsii, GITTL, M., 1950

[12] Fedoryuk M. V., Asimptotika. Integraly i ryady, Nauka, M., 1987

[13] Akchurin E. R., Minlos R. A., “Teoriya rasseyaniya dlya odnogo klassa dvuchastichnykh operatorov matematicheskoi fiziki (sluchai slabogo vzaimodeistviya)”, Izv. RAN (to appear)

[14] Gelfand I. M., Raikov D. A., Shilov G. E., Kommutativnye normirovannye koltsa, Gostekhizdat, M., 1960

[15] Paraska V. I., Mat. sb., 68(110):4 (1965), 623–631 | MR | Zbl