On the essential and the discrete spectra of a~Fredholm type partial integral operator
Matematičeskie trudy, Tome 17 (2014) no. 2, pp. 23-40.

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We investigate the structure of the essential spectrum of a self-adjoint Fredholm type partial integral operator $H$. We obtain an explicit description of the essential spectrum of $H$ and prove that an eigenvalue of $H$ exists.
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G. P. Arzikulov; Yu. Kh. Eshkabilov. On the essential and the discrete spectra of a~Fredholm type partial integral operator. Matematičeskie trudy, Tome 17 (2014) no. 2, pp. 23-40. http://geodesic.mathdoc.fr/item/MT_2014_17_2_a1/

[1] Vekua I. N., Novye metody resheniya ellipticheskikh uravnenii, OGIZ, M.–L., 1948 | MR

[2] Gursa E., Kurs matematicheskogo analiza, v. 3{, Ch. 2}, Integralnye uravneniya. Variatsionnoe ischislenie, GTTI, M.–L., 1934

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

[4] Kalitvin A. S., Lineinye operatory s chastnymi integralami, TsChKI, Voronezh, 2000

[5] Kalitvin A. S., Frolova E. V., Lineinye uravneniya s chastnymi integralami. $C$-teoriya, LGPU, Lipetsk, 2004

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

[7] Lakshtanov E. A., Minlos R. A., “Spektr dvukhchastichnykh svyazannykh sostoyanii transfer-matrits gibbsovskikh polei (uedinennoe svyazannoe sostoyanie)”, Funkts. analiz i ego pril., 38:3 (2004), 52–69 | DOI | MR | Zbl

[8] 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

[9] Myuntts G., Integralnye uravneniya, v. 1, Lineinye uravneniya, Gostekhteorizdat, L.–M., 1934

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

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

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

[13] Trikomi F., Integralnye uravneniya, Izd-vo inostr. lit., M., 1960 | MR

[14] Eshkabilov Yu. Kh., “Vozmuschenie spektra operatora umnozheniya na funktsiyu s chastnym integralnym operatorom”, Vestnik nats. un-ta Uzbekistana, 2006, no. 2, 17–21 | MR

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

[16] Eshkabilov Yu. Kh., “Suschestvennyi i diskretnyi spektry chastichno integralnykh operatorov”, Matem. tr., 11:2 (2008), 187–203 | MR

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

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

[19] Eshkabilov Yu. Kh., Chastichno integralnye operatory tipa Fredgolma, LAP, Saarbrücken, 2013

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

[21] 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

[22] Aleksandrov V. M., Kovalenko E. V., “One class of integral equations in mixed problems of the mechanics of continuous media”, Soviet Phys. Dokl., 25:2 (1980), 354–356 | Zbl

[23] Aleksandrov V. M., Kovalenko E. V., “Contact interaction of bodies with coatings in the presence of abrasion”, Soviet Phys. Dokl., 4:29 (1984), 340–342

[24] Appell J., Kalitvin A. S., Nashed M. Z., “On some partial integral equations arising in the mechanics of solids”, Z. Angew. Math. Mech., 79:10 (1999), 703–713 | 3.0.CO;2-W class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[25] Appell J., Kalitvin A. S., Zabrejko P. P., Partial Integral Operators and Integro-Differential Equations, Monographs and Textbooks in Pure and Applied Mathematics, 230, Marcel Dekker, Inc., New York, 2000 | MR | Zbl

[26] Manzhirov A. V., “On a method of solving two-dimensional integral equations of axisymmetric contact problems for bodies with complex rheology”, J. Appl. Math. Mech., 49:6 (1985), 777–782 | DOI | MR | Zbl