Geodesic
Completeness of the Root Function System of a Nonlocal Problem in $L_p$
Matematičeskie zametki, Tome 71 (2002) no. 6, pp. 878-889.

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We obtain sufficient conditions for the completeness of the root function system for nonlocal elliptic problems in the Sobolev spaces $W_p^l(Q)$. 
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V. V. Pod'yapol'skii. Completeness of the Root Function System of a Nonlocal Problem in $L_p$. Matematičeskie zametki, Tome 71 (2002) no. 6, pp. 878-889. http://geodesic.mathdoc.fr/item/MZM_2002_71_6_a7/

[1] Tamarkin Ya. D., O nekotorykh obschikh zadachakh teorii obyknovennykh lineinykh differentsialnykh uravnenii i o razlozhenii proizvolnykh funktsii v ryady, Tipografiya M. P. Frolovoi, Petrograd, 1917

[2] Krall A. M., “The development of general differential and general boundary systems”, Rocky Mountain J. Math., 5 (1972), 493–542 | MR

[3] Ilin V. A., “Neobkhodimye i dostatochnye usloviya bazisnosti Rissa kornevykh vektorov razryvnykh operatorov vtorogo poryadka”, Differents. uravneniya, 22:12 (1986), 2059–2071 | MR | Zbl

[4] Shkalikov A. A., “O bazisnosti sobstvennykh funktsii obyknovennykh differentsialnykh operatorov s integralnymi kraevymi usloviyami”, Vestn. MGU. Ser. 1. Matem., mekh., 1982, no. 6, 12–21 | MR | Zbl

[5] Skubachevskii A. L., “Nelokalnye ellipticheskie zadachi s parametrom”, Matem. sb., 121:6 (1983), 201–210 | MR

[6] Browder F., “Asymptotic distribution of eigenvalues and eigenfunctions for nonlocal elliptic boundary value problems”, Amer. J. Math., 87:1 (1965), 175–195 | DOI | MR | Zbl

[7] Moiseev E. I., “O spektralnykh kharakteristikakh odnoi nelokalnoi kraevoi zadachi”, Differents. uravneniya, 30:5 (1994), 864–872 | MR | Zbl

[8] Moiseev E. I., “Ob otsutstvii svoistva bazisnosti u sistemy kornevykh funktsii odnoi nelokalnoi kraevoi zadachi”, Differents. uravneniya, 30:12 (1994), 2082–2093 | MR | Zbl

[9] Lidskii V. B., “O summiruemosti ryadov po glavnym vektoram nesamosopryazhennykh operatorov”, Tr. MMO, 11, URSS, M., 1962, 3–35 | MR

[10] Kovaleva O. A., Skubachevskii A. L., “Nelokalnye ellipticheskie zadachi v prostranstvakh Soboleva $W^l_p(Q)$”, Dokl. RAN, 366:4 (1999), 449–451 | MR | Zbl

[11] Agranovich M., Denk R., Faierman M., Weakly Smooth Nonselfadjoint Spectral Elliptic Boundary Problems, Advances in Partial Differential Equations, Math. Topics, 14, Akademie Verlag, Berlin, 1997 | Zbl

[12] Agmon S., “On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems”, Comm. Pure Appl. Math., 15 (1962), 119–147 | DOI | MR | Zbl

[13] Levin B. Ya., Raspredelenie kornei tselykh funktsii, GITTL, M., 1956

[14] Boimatov K. Kh., Kostyuchenko A. G., “Spektralnaya asimptotika nesamosopryazhennykh ellipticheskikh sistem differentsialnykh operatorov v ogranichennykh oblastyakh”, Matem. sb., 181:12 (1990), 1678–1693