Sufficient condition of Hilbertness of some eigenfunctions systems of the second order differential operator
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 115 (2007) no. 2, pp. 158-161 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We obtain the sufficient condition of Hilbertness for the systems of eigenfunctions of the ordinary linear non-selfjoined differential operator of the second order with the condition that the imaginary parts of spectral parameters are large enough by absolute value.
@article{VSGTU_2007_115_2_a22,
     author = {A. S. Tsareva},
     title = {Sufficient condition of {Hilbertness} of some eigenfunctions systems of the second order differential operator},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {158--161},
     year = {2007},
     volume = {115},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2007_115_2_a22/}
}
TY  - JOUR
AU  - A. S. Tsareva
TI  - Sufficient condition of Hilbertness of some eigenfunctions systems of the second order differential operator
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2007
SP  - 158
EP  - 161
VL  - 115
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2007_115_2_a22/
LA  - ru
ID  - VSGTU_2007_115_2_a22
ER  - 
%0 Journal Article
%A A. S. Tsareva
%T Sufficient condition of Hilbertness of some eigenfunctions systems of the second order differential operator
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2007
%P 158-161
%V 115
%N 2
%U http://geodesic.mathdoc.fr/item/VSGTU_2007_115_2_a22/
%G ru
%F VSGTU_2007_115_2_a22
A. S. Tsareva. Sufficient condition of Hilbertness of some eigenfunctions systems of the second order differential operator. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 115 (2007) no. 2, pp. 158-161. http://geodesic.mathdoc.fr/item/VSGTU_2007_115_2_a22/

[1] Bari N. K., “Biortogonalnye sistemy i bazisy v gilbertovom prostranstve”, Matematika, Tom IV, Uch. zap. MGU, 148, 1951, 69–107 | MR

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

[3] Ilin V. A., “Neravenstvo tipa Gilberta po sisteme sobstvennykh funktsii operatora Laplasa dlya radialnoi funktsii, otlichnoi ot nulya v share dostatochno malogo radiusa”, Dokl. AN SSSR, 291:6 (1986), 1292–1296 | MR

[4] Budaev V. D., “O neravenstvakh Gilberta i Besselya dlya nekotorykh vozmuschënnykh sistem funktsii”, Polianaliticheskie funktsii: granichnye svoistva i kraevye zadachi, Mezhvuz. sb. nauch. tr., SGPI, Smolensk, 1997, 100–107

[5] Malov A. A., “Dostatochnye usloviya vypolneniya neravenstva tipa Gilberta po sisteme kornevykh funktsii obyknovennogo differentsialnogo operatora vtorogo poryadka”, Differents. uravneniya, 30:2 (1994), 197–203 | MR | Zbl

[6] Budaev V. D., Bezuslovnaya bazisnost sistem kornevykh funktsii obyknovennykh differentsialnykh operatorov, Dis. ... d-ra. fiz.-mat. nauk. 01.02.04, MGU, M., 1993

[7] Tikhomirov V. V., “Tochnye otsenki regulyarnogo resheniya odnomernogo uravneniya Shredingera so spektralnym parametrom”, Dokl. AN SSSR, 273:4 (1983), 807–810 | MR | Zbl

[8] Tikhomirov V. V., “Tochnye otsenki sobstvennykh funktsii proizvolnogo nesamosopryazhennogo operatora Shredingera”, Differents. uravneniya, 19:8 (1983), 1378–1385 | MR | Zbl

[9] Tsareva A. S., “Nekotorye otsenki norm kornevykh funktsii differentsialnogo operatora vtorogo poryadka”, Issledovaniya po kraevym zadacham kompleksnogo analiza i differentsialnym uravneniyam, Mezhvuz. sb. nauch. tr., 7, SmolGU, Smolensk, 2006, 106–116

[10] Bilalov B. T., Bazisnye svoistva sistem sobstvennykh funktsii nekotorykh differentsialnykh operatorov i ikh obobschenie, Dis. ... d-ra. fiz.-mat. nauk. 01.02.04, MGU, M., 1995