Completeness of eigenfunctions of one class of pencils of differential operators with constant coefficients
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2009), pp. 42-53.

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In this paper, in spaces of functions square summable on finite intervals we study the one-fold completeness of the system of eigen- and associated functions for the pencil of ordinary differential operators generated by a differential expression with constant coefficients (we assume that the roots of the corresponding characteristic equation lie on one and the same ray) and specific semisplitting homogeneous boundary value conditions.
Keywords: multiple completeness, one-fold completeness, eigen- and associated functions, pencil of ordinary differential operators.
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V. S. Rykhlov. Completeness of eigenfunctions of one class of pencils of differential operators with constant coefficients. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2009), pp. 42-53. http://geodesic.mathdoc.fr/item/IVM_2009_6_a5/

[1] Naimark M. A., Lineinye differentsialnye operatory, Nauka, M., 1969, 528 pp. | MR | Zbl

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

[3] Gasymov M. G., Magerramov A. M., “O kratnoi polnote sistemy sobstvennykh i prisoedinennykh funktsii odnogo klassa differentsialnykh operatorov”, DAN AzSSR, 30:3 (1974), 9–12 | MR | Zbl

[4] Keldysh M. V., “O sobstvennykh znacheniyakh i sobstvennykh funktsiyakh nekotorykh klassov nesamosopryazhennykh uravnenii”, DAN SSSR, 77:1 (1951), 11–14 | Zbl

[5] Khromov A. P., Konechnomernye vozmuscheniya volterrovykh operatorov, Dis. $\dots$ dokt. fiz.-matem. nauk, Novosibirsk, 1973, 242 pp.

[6] Shkalikov A. A., “O polnote sobstvennykh i prisoedinennykh funktsii obyknovennogo differentsialnogo operatora s neregulyarnymi kraevymi usloviyami”, Funkts. analiz i ego pril., 10:4 (1976), 69–80 | MR | Zbl

[7] Eberhard W., “Zur Vollständigkeit des Biorthogonalsystems von Eigenfunktionen irregulärer Eigenwertprobleme”, Math. Z., 146:3 (1976), 213–221 | DOI | MR

[8] Freiling G., “Zur Vollständigkeit des Systems der Eigenfunktionen und Hauptfunktionen irregulärer Operator-büschel”, Math. Z., 188:1 (1984), 55–68 | DOI | MR | Zbl

[9] Vagabov A. I., Razlozheniya v ryady Fure po glavnym funktsiyam differentsialnykh operatorov i ikh primeneniya, Dis. $\dots$ dokt. fiz.-matem. nauk, M., 1988, 201 pp.

[10] Vagabov A. I., Vvedenie v spektralnuyu teoriyu differentsialnykh operatorov, Izd-vo Rostovsk. un-ta, Rostov-na-Donu, 1994, 160 pp.

[11] Rykhlov V. S., “O kratnoi nepolnote sobstvennykh funktsii puchkov obyknovennykh differentsialnykh operatorov”, Matem. Mekhan. Sb. nauch. tr., 3, Izd-vo Sarat. un-ta, Saratov, 2001, 114–117

[12] Rykhlov V. S., “O kratnoi nepolnote sobstvennykh funktsii puchkov differentsialnykh operatorov, korni kharakteristicheskogo uravneniya kotorykh lezhat na odnom luche”, Dokl. RAEN, No 4, Izd-vo Saratovsk. gos. tekhn. un-ta, Saratov, 2004, 72–79

[13] Rykhlov V. S., “O polnote sobstvennykh funktsii puchkov obyknovennykh differentsialnykh operatorov”, Uchen. zap. Tavrichesk. natsion. un-ta. Ser. Matem. Mekhan. Informatika i kibernetika, 2006, no. 2, 78–81

[14] Rykhlov V. S., “O polnote sobstvennykh funktsii kvadratichnykh puchkov obyknovennykh differentsialnykh operatorov”, Izv. vuzov. Matematika, 1992, no. 3, 35–44 | MR | Zbl

[15] Rykhlov V. S., “O svoistvakh sobstvennykh funktsii obyknovennogo differentsialnogo kvadratichnogo puchka vtorogo poryadka”, Integralnye preobrazovaniya i spetsialnye funktsii, Informatsionnyi byulleten. T. 2, No 1, Nauchno-issledovatelskaya gruppa mezhdunarodnogo zhurnala “Integral Transforms and Special Functions” i VTs RAN., M., 2001, 85–103