Geodesic
Essential spectrum of a model operator associated with a three-particle system on a lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 166 (2011) no. 1, pp. 95-109
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider a model operator $H$ associated with the system of three particles interacting via nonlocal pair potentials on a $\nu$-dimensional lattice. We identify channel operators and use their spectra to describe the position and structure of the essential spectrum of $H$. We obtain an analogue of the Faddeev equation for the eigenfunctions of $H$.
Keywords: model operator, nonlocal potential, Hilbert–Schmidt class, Faddeev equation, essential spectrum, channel operator. 
@article{TMF_2011_166_1_a6,
     author = {T. H. Rasulov},
     title = {Essential spectrum of a~model operator associated with a~three-particle system on a~lattice},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {95--109},
     year = {2011},
     volume = {166},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_166_1_a6/}
}
TY  - JOUR
AU  - T. H. Rasulov
TI  - Essential spectrum of a model operator associated with a three-particle system on a lattice
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2011
SP  - 95
EP  - 109
VL  - 166
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2011_166_1_a6/
LA  - ru
ID  - TMF_2011_166_1_a6
ER  - 
%0 Journal Article
%A T. H. Rasulov
%T Essential spectrum of a model operator associated with a three-particle system on a lattice
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2011
%P 95-109
%V 166
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2011_166_1_a6/
%G ru
%F TMF_2011_166_1_a6
T. H. Rasulov. Essential spectrum of a model operator associated with a three-particle system on a lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 166 (2011) no. 1, pp. 95-109. http://geodesic.mathdoc.fr/item/TMF_2011_166_1_a6/

[1] M. Rid, B. Saimon, Metody sovremennoi matematicheskoi fiziki, v. 4, Analiz operatorov, Mir, M., 1982 | MR | MR | Zbl

[2] G. M. Zhislin, Trudy MMO, 9, 1960, 81–120 | MR | Zbl

[3] W. Hunziker, Helv. Phys. Acta, 39 (1966), 451–462 | MR | Zbl

[4] S. N. Lakaev, M. E. Muminov, TMF, 135:3 (2003), 478–503 | DOI | MR | Zbl

[5] S. Albeverio, S. N. Lakaev, Z. I. Muminov, Math. Nachr., 280:7 (2007), 699–716, arXiv: math-ph/0312050 | DOI | MR | Zbl

[6] S. Albeverio, S. N. Lakaev, Z. I. Muminov, Russ. J. Math. Phys., 14:4 (2007), 377–387 | DOI | MR | Zbl

[7] S. Albeverio, S. N. Lakaev, R. Kh. Djumanova, Rep. Math. Phys., 63:3 (2009), 359–380 | DOI | MR | Zbl

[8] V. Kheine, M. Koen, D. Ueir, Teoriya psevdopotentsiala, Mir, M., 1973

[9] T. Kh. Rasulov, TMF, 163:1 (2010), 34–44 | DOI | MR | Zbl

[10] R. L. Hall, J. Phys. A, 39:4 (2006), 903–912, arXiv: math-ph/0512079 | DOI | MR | Zbl

[11] K. Chadan, R. Kobayashi, J. Phys. A, 38:5 (2005), 1133–1145, arXiv: math-ph/0409018 | DOI | MR | Zbl

[12] Zh. I. Abdullaev, Uzb. matem. zhurn., 1996, no. 1, 3–10 | MR

[13] T. Kh. Rasulov, Izv. vuzov. Matem., 2008, no. 12, 59–69 | DOI | MR | Zbl

[14] Yu. Kh. Eshkabilov, TMF, 149:2 (2006), 228–243 | DOI | MR | Zbl