Riesz Bases of Eigenfunctions of an Integral Operator with a~Variable Limit of Integration
Matematičeskie zametki, Tome 76 (2004) no. 1, pp. 97-110.

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We prove a theorem on the Riesz basis property in the space $L_2[0,1]$ of the eigenfunctions and associated functions of an integral operator whose kernel possesses a derivative discontinuous on the line $t=1-x$.
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V. P. Kurdyumov; A. P. Khromov. Riesz Bases of Eigenfunctions of an Integral Operator with a~Variable Limit of Integration. Matematičeskie zametki, Tome 76 (2004) no. 1, pp. 97-110. http://geodesic.mathdoc.fr/item/MZM_2004_76_1_a9/

[1] Khromov A. P., “Ob obraschenii integralnykh operatorov s yadrami, razryvnymi na diagonalyakh”, Matem. zametki, 64:6 (1998), 932–942 | MR | Zbl

[2] Khromov A. P., “Teorema ravnoskhodimosti dlya integralnogo operatora s peremennym verkhnim predelom integrirovaniya”, Sb. statei, posvyaschennyi 70-letiyu P. L. Ulyanova, M., 1999, 255–266 | MR

[3] Kornev V. V., Khromov A. P., “O ravnoskhodimosti razlozhenii po sobstvennym funktsiyam integralnykh operatorov s yadrami, dopuskayuschimi razryvy proizvodnykh na diagonalyakh”, Matem. sb., 192:10 (2001), 33–50 | MR | Zbl

[4] Mikhailov V. P., “O bazisakh Rissa v $L_2[0,1]$”, Dokl. AN SSSR, 144:5 (1962), 981–984 | MR

[5] Keselman G. M., “O bezuslovnoi skhodimosti razlozhenii po sobstvennym funktsiyam nekotorykh differentsialnykh operatorov”, Izv. vuzov. Matem., 1964, no. 2, 82–93 | MR | Zbl

[6] Danford N., Shvarts Dzh. T., Lineinye operatory, T. 3, Mir, M., 1974

[7] Shkalikov A. A., “O bazisnosti sobstvennykh funktsii obyknovennogo differentsialnogo operatora”, UMN, 34:5 (1979), 235–236 | MR | Zbl

[8] Shkalikov A. A., “O bazisnosti sobstvennykh funktsii obyknovennykh differentsialnykh operatorov s integralnymi kraevymi usloviyami”, Vestn. MGU. Ser. matem., mekh., 1982, no. 6, 12–21 | MR | Zbl

[9] Shkalikov A. A., “Kraevye zadachi dlya obyknovennykh differentsialnykh uravnenii s parametrom v granichnykh usloviyakh”, Tr. sem. im. I. G. Petrovskogo, 9, Izd-vo Mosk. un-ta, M., 1983, 190–229 | MR | Zbl

[10] Gomilko A. M., Radzievskii G. V., “Bazisnye svoistva sobstvennykh funktsii regulyarnoi kraevoi zadachi dlya vektornogo funktsionalno-differentsialnogo uravneniya”, Differents. uravneniya, 27:3 (1991), 384–396 | MR | Zbl

[11] Radzievskii G. V., “Kraevye zadachi i svyazannye s nimi moduli nepreryvnosti”, Funktsion. analiz i ego prilozh., 29:3 (1995), 87–90 | MR | Zbl

[12] Baskakov A. G., Katsaran T. K., “Spektralnyi analiz integro-differentsialnykh operatorov s nelokalnymi kraevymi usloviyami”, Differents. uravneniya, 24:8 (1988), 1424–1433 | MR | Zbl

[13] Ilin V. A., “Neobkhodimye i dostatochnye usloviya bazisnosti v $L_p$ i ravnoskhodimosti s trigonometricheskim ryadom spektralnykh razlozhenii i razlozhenii po sistemam eksponent”, Dokl. AN SSSR, 273:4 (1983), 789–793 | MR | Zbl

[14] Ilin V. A., “Neobkhodimye i dostatochnye usloviya bazisnosti i ravnoskhodimosti s trigonometricheskim ryadom spektralnykh razlozhenii, I”, Differents. uravneniya, 16:5 (1980), 771–794 | MR | Zbl

[15] Ilin V. A., “Neobkhodimye i dostatochnye usloviya bazisnosti i ravnoskhodimosti s trigonometricheskim ryadom spektralnykh razlozhenii, II”, Differents. uravneniya, 16:6 (1980), 980–1009 | MR | Zbl

[16] Paltsev B. V., “Razlozheniya po sobstvennym funktsiyam integralnykh operatorov svertki na konechnom intervale s yadrami, preobrazovaniya Fure kotorykh ratsionalny. “Slabo nesamosopryazhennye regulyarnye yadra””, Izv. AN SSSR. Ser. matem., 36:3 (1972), 591–634 | MR | Zbl

[17] Kurdyumov V. P., Neobkhodimye i dostatochnye usloviya optimalnosti dlya differentsialno-operatornogo uravneniya, Dep. VINITI 02.07.85 No. 4781, Sarat. un-t, Saratov, 1985

[18] Kurdyumov V. P., “O bazisakh Rissa iz sobstvennykh i prisoedinennykh funktsii nekotorykh integralnykh operatorov”, Differents. uravneniya, 38:4 (2002), 555–564 | MR | Zbl

[19] Khromov A. P., “Teoremy ravnoskhodimosti dlya integro-differentsialnykh i integralnykh operatorov”, Matem. sb., 114 (156):3 (1981), 378–405 | MR | Zbl

[20] Naimark M. A., Lineinye differentsialnye operatory, Nauka, M., 1969