The Faddeev equation and location of the essential spectrum of a three-particle model operator
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2011), pp. 170-180.

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

In this paper a model operator $H$ associated to a system of three-particles on a lattice is considered. The location of the essential spectrum of $H$ is described by the spectrum of channel operators. The Faddeev type equation for the eigenvectors of $H$ is obtained.
Keywords: model operator, essential spectrum, channel operator, Faddeev equation.
@article{VSGTU_2011_2_a21,
     author = {T. Kh. Rasulov and A. A. Rakhmonov},
     title = {The {Faddeev} equation and location of the essential spectrum of a three-particle model operator},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {170--180},
     publisher = {mathdoc},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2011_2_a21/}
}
TY  - JOUR
AU  - T. Kh. Rasulov
AU  - A. A. Rakhmonov
TI  - The Faddeev equation and location of the essential spectrum of a three-particle model operator
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2011
SP  - 170
EP  - 180
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2011_2_a21/
LA  - ru
ID  - VSGTU_2011_2_a21
ER  - 
%0 Journal Article
%A T. Kh. Rasulov
%A A. A. Rakhmonov
%T The Faddeev equation and location of the essential spectrum of a three-particle model operator
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2011
%P 170-180
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2011_2_a21/
%G ru
%F VSGTU_2011_2_a21
T. Kh. Rasulov; A. A. Rakhmonov. The Faddeev equation and location of the essential spectrum of a three-particle model operator. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2011), pp. 170-180. http://geodesic.mathdoc.fr/item/VSGTU_2011_2_a21/

[1] Reed M., Simon B., Methods of modern mathematical physics, v. IV, Analysis of operators, Academic Press, New York–London, 1978, 396 pp. ; Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, v. 4, Analiz operatorov, Mir, M., 1982, 430 pp. | MR | Zbl | MR | Zbl

[2] Zhislin G. M., “Investigations of the spectrum of the Schrödinger operator for a many body system”, Trudy Mosk. Mat. Obsh-va, 9 (1960), 81–120 | Zbl

[3] Albeverio S., Lakaev S. N., Muminov Z. I., “Schrödinger operators on lattices. The Efimov effect and discrete spectrum asymptotics”, Ann. Henri Poincaré, 5:4 (2004), 743–772 | MR | Zbl

[4] Albeverio S., Lakaev S. N., Muminov Z. I., “On the structure of the essential spectrum for the three-particle Schrödinger operators on lattices”, Math. Nachr., 280:7 (2007), 699–716 | DOI | MR | Zbl

[5] Albeverio S., Lakaev S. N., Muminov Z. I., “On the number of eigenvalues of a model operator associated to a system of three-particles on lattices”, Russ. J. Math. Phys., 14:4 (2007), 377–387 | DOI | MR | Zbl

[6] Albeverio S., Lakaev S. N., Djumanova R. Kh., “The essential and discrete spectrum of a model operator associated to a system of three identical quantum particles”, Reports on Math. Phys., 63:3 (2009), 359–380 | DOI | MR | Zbl

[7] Rasulov T. Kh., “Asymptotics of the discrete spectrum of a model operator associated with a system of three particles on a lattice”, Theoret. and Math. Phys., 163:1 (2010), 429–437 | DOI | DOI | Zbl

[8] Faddeev L. D., “Mathematical questions in the quantum theory of scattering for a system of three particles”, Trudy Mat. Inst. Steklov., 69, Acad. Sci. USSR, Moscow–Leningrad, 1963, 3–122 | MR