Geodesic
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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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/
@article{IVM_2009_6_a5,
     author = {V. S. Rykhlov},
     title = {Completeness of eigenfunctions of one class of pencils of differential operators with constant coefficients},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {42--53},
     year = {2009},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_6_a5/}
}
TY  - JOUR
AU  - V. S. Rykhlov
TI  - Completeness of eigenfunctions of one class of pencils of differential operators with constant coefficients
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2009
SP  - 42
EP  - 53
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/IVM_2009_6_a5/
LA  - ru
ID  - IVM_2009_6_a5
ER  - 
%0 Journal Article
%A V. S. Rykhlov
%T Completeness of eigenfunctions of one class of pencils of differential operators with constant coefficients
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2009
%P 42-53
%N 6
%U http://geodesic.mathdoc.fr/item/IVM_2009_6_a5/
%G ru
%F 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