Geodesic
Essential and discrete spectra of the three-particle Schrödinger operator on a lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 170 (2012) no. 3, pp. 409-422 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the position of the essential spectrum of a three-body Schrödinger operator $H$. We evaluate the lower boundary of the essential spectrum of $H$ and prove that the number of eigenvalues located below the lower edge of the essential spectrum in the $H$ model is finite.
Keywords: essential spectrum, discrete spectrum, lower boundary of the essential spectrum, Schrödinger operator. 
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     title = {Essential and discrete spectra of the~three-particle {Schr\"odinger} operator on a~lattice},
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Yu. Kh. Eshkabilov; R. R. Kucharov. Essential and discrete spectra of the three-particle Schrödinger operator on a lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 170 (2012) no. 3, pp. 409-422. http://geodesic.mathdoc.fr/item/TMF_2012_170_3_a6/

[1] J. Uchiyama, Publ. Res. Inst. Math. Sci., 5:1 (1969), 51–63 | DOI | MR | Zbl

[2] J. Uchiyama, Publ. Res. Inst. Math. Sci., 6:1 (1970), 189–192 | DOI | MR | Zbl

[3] J. Uchiyama, Publ. Res. Inst. Math. Sci., 6:1 (1970), 193–200 | DOI | MR | Zbl

[4] G. M. Zhislin, TMF, 7:3 (1971), 332–341 | DOI | Zbl

[5] D. R. Yafaev, Dokl. AN SSSR, 206 (1972), 68–70 | MR

[6] D. R. Yafaev, Tochechnyi spektr v kvantomekhanicheskoi zadache trekh chastits, dis. $\dots$ kand. fiz.-matem. nauk, LGU, L., 1973

[7] G. M. Zhislin, Dokl. AN SSSR, 207 (1972), 25–28 | Zbl

[8] G. M. Zhislin, TMF, 21:1 (1974), 60–73 | DOI | MR

[9] G. M. Zhislin, Izv. AN SSSR. Ser. matem., 33:3 (1969), 590–649 | DOI | MR | Zbl

[10] A. G. Sigalov, I. M. Sigal, TMF, 5:1 (1970), 73–93 | DOI | MR

[11] D. C. Mattis, Rev. Modern Phys., 58:2 (1986), 361–379 | DOI | MR

[12] A. I. Mogilner, “Hamiltonians in solid-state physics as multiparticle discrete Schrodinger operators: problems and results”, Many Particle Hamiltonians: Spectra and Scattering, Advances in Soviet Mathematics, 5, ed. R. A. Minlos, AMS, Providence, RI, 1991, 139–194 | MR | Zbl

[13] M. Rid, B. Saimon, Metody sovremennoi matematicheskoi fiziki, v. 3, Teoriya rasseyaniya, Mir, M., 1982 | MR | Zbl

[14] S. N. Lakaev, R. A. Minlos, TMF, 39:1 (1979), 83–93 | DOI | MR

[15] V. A. Malyshev, R. A. Minlos, Lineinye operatory v beskonechnochastichnykh sistemakh, Fizmatlit, M., 1994 | MR

[16] S. N. Lakaev, TMF, 91:1 (1992), 51–65 | DOI | MR

[17] Yu. V. Zhukov, TMF, 107:1 (1996), 75–85 | DOI | MR | Zbl

[18] Zh. I. Abdullaev, S. N. Lakaev, TMF, 111:1 (1997), 94–108 | DOI | MR | Zbl

[19] S. N. Lakaev, S. M. Samatov, TMF, 129:3 (2001), 415–431 | DOI | MR | Zbl

[20] S. Albeverio, S. N. Lakaev, J. I. Abdullaev, Rep. Math. Phys., 51:1 (2003), 43–70 | DOI | MR | Zbl

[21] S. N. Lakaev, S. M. Samatov, UMN, 57:1(343) (2002), 155–156 | DOI | MR | Zbl

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

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

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

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

[26] Yu. Kh. Eshkabilov, TMF, 164:1 (2010), 78–87 | DOI | Zbl

[27] F. Dzh. Trikomi, Integralnye uravneniya, IL, M., 1960 | MR | Zbl

[28] Yu. Kh. Eshkabilov, Matem. trudy, 11:2 (2008), 187–203 | MR | Zbl

[29] Yu. Kh. Eshkabilov, Vestn. NUUz, 2 (2006), 17–21

[30] L. D. Faddeev, Tr. MIAN SSSR, 73 (1964), 292–313 | MR | Zbl

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

[32] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1981 | MR | Zbl