On the discrete spectrum of partial integral operators
Matematičeskie trudy, Tome 15 (2012) no. 2, pp. 194-203.

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We prove a theorem on the discrete spectrum of a partial integral selfadjoint operator with a continuous kernel.
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Yu. Kh. Eshkabilov. On the discrete spectrum of partial integral operators. Matematičeskie trudy, Tome 15 (2012) no. 2, pp. 194-203. http://geodesic.mathdoc.fr/item/MT_2012_15_2_a11/

[1] Zhukov Yu. V., “Teorema Iorio–O'Kerrola dlya $N$-chastichnogo reshetchatogo gamiltoniana”, TMF, 107:1 (1996), 75–85 | DOI | MR | Zbl

[2] Kalitvin A. S., “O spektre lineinykh operatorov s chastnymi integralami i polozhitelnymi yadrami”, Operatory i ikh prilozheniya, Mezhvuzovskii. sb. nauch. tr., Leningradskii gos. ped. in-t, Leningrad, 1988, 43–50 | MR | Zbl

[3] Likhtarnikov L. M., Vitova L. Z., “O spektre integralnogo operatora s chastnymi integralami”, Litovsk. matem. sb., 15:2 (1975), 41–47 | MR | Zbl

[4] Malyshev V. A., Minlos R. A., “Klasternye operatory”, Tr. seminara im. I. G. Petrovskogo, 9, Izd-vo Mosk. un-ta, M., 1983, 63–80 | MR

[5] Rasulov T. Kh., “Asimptotika diskretnogo spektra odnogo modelnogo operatora, assotsiirovannogo s sistemoi trekh chastits na reshetke”, TMF, 163:1 (2010), 34–44 | DOI | Zbl

[6] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, v. 1, Funktsionalnyi analiz, Mir, M., 1977 | MR

[7] Smirnov V. I., Kurs vysshei matematiki, Ch. I, v. 4, Nauka, M., 1974 | MR

[8] Eshkabilov Yu. Kh., Dva elektrona v primesnoi modeli Khabbarda. Ch. 1: Tripletnoe sostoyanie, Dep. v GFNTI GKNT RUz, No 2148-Uz94, 08.07.1994

[9] Eshkabilov Yu. Kh., “Ob odnom diskretnom “trekhchastichnom” operatore Shredingera v modeli Khabbarda”, TMF, 149:2 (2006), 228–243 | DOI | MR | Zbl

[10] Eshkabilov Yu. Kh., “Chastichno integralnyi operator s ogranichennym yadrom”, Matem. tr., 11:1 (2008), 192–207 | MR | Zbl

[11] Eshkabilov Yu. Kh., “Effekt Efimova dlya odnogo modelnogo “trekhchastichnogo” diskretnogo operatora Shredingera”, TMF, 164:1 (2010), 78–87 | DOI | Zbl

[12] Eshkabilov Yu. Kh., “O beskonechnosti diskretnogo spektra operatorov v modeli Fridrikhsa”, Matem. tr., 14:1 (2011), 195–211 | MR | Zbl

[13] Eshkabilov Yu. Kh., Kucharov R. R., “O suschestvennom i diskretnom spektrakh trekhchastichnogo operatora Shredingera na reshetke”, TMF, 170:3 (2012), 409–422 | DOI

[14] Eshkabilov Yu. Kh., Sakhobidinova O. I., “O beskonechnosti diskretnogo spektra operatorov v modeli Fridrikhsa”, Matematicheskii forum, Itogi nauki. Yug Rossii, v. 1, Issledovaniya po matematicheskomu analizu, VNTs RAN, Vladikavkaz, 2008, 246–255

[15] 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”, Russian J. Math. Phys., 14:4 (2007), 377–387 | DOI | MR | Zbl

[16] Eshkabilov Yu. Kh., “Spectra of partial integral operators with a kernel of three variables”, Central European J. Math., 6:1 (2008), 149–157 | DOI | MR | Zbl

[17] Kalitvin A. S., Zabrejko P. P., “On the theory of partial integral operators”, J. Integral Equations Appl., 3:3 (1991), 351–382 | DOI | MR | Zbl

[18] Mattis D. C., “The few-body problem on a lattice”, Rev. Modern Phys., 58:2 (1986), 361–379 | DOI | MR

[19] Mogilner A. I., “The problem of a few quasi-particles in solid-state physics”, Application of Self-Adjoint Extensions in Quantum Physics, Lecture Notes Phys., 324, eds. P. Exner, P. Seba, Springer-Verlag, Berlin, 1988, 160–173

[20] Mogilner A. I., “Hamiltonians in solid-state physics as multiparticle discrete Schrödinger operators: problems and results”, Adv. Soviet Math., 5, Amer. Math. Soc., Providence, RI, 1991, 139–194 | MR