Geodesic
Stability of the Schmidt orthogonalization operator
Izvestiya. Mathematics, Tome 4 (1970) no. 4, pp. 811-834 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this article we prove the existence of points of local instability of the Schmidt orthogonalization operator and classify them. We establish the quadratic stability of this operator in a neighborhood of a fixed point. 
@article{IM2_1970_4_4_a6,
     author = {A. M. Olevskii},
     title = {Stability of the {Schmidt} orthogonalization operator},
     journal = {Izvestiya. Mathematics},
     pages = {811--834},
     year = {1970},
     volume = {4},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1970_4_4_a6/}
}
TY  - JOUR
AU  - A. M. Olevskii
TI  - Stability of the Schmidt orthogonalization operator
JO  - Izvestiya. Mathematics
PY  - 1970
SP  - 811
EP  - 834
VL  - 4
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/IM2_1970_4_4_a6/
LA  - en
ID  - IM2_1970_4_4_a6
ER  - 
%0 Journal Article
%A A. M. Olevskii
%T Stability of the Schmidt orthogonalization operator
%J Izvestiya. Mathematics
%D 1970
%P 811-834
%V 4
%N 4
%U http://geodesic.mathdoc.fr/item/IM2_1970_4_4_a6/
%G en
%F IM2_1970_4_4_a6
A. M. Olevskii. Stability of the Schmidt orthogonalization operator. Izvestiya. Mathematics, Tome 4 (1970) no. 4, pp. 811-834. http://geodesic.mathdoc.fr/item/IM2_1970_4_4_a6/

[1] Kachmazh S., Shteingauz G., Teoriya ortogonalnykh ryadov, Fizmatgiz, M., 1958 | MR

[2] Szlenk W., “Une remark sur l'orthogonalisation des bases de Schauder dans l'espace $C$”, Colloq. math., 15:2 (1966), 297–301 | MR | Zbl

[3] Krein M., Milman D., Rutman M., “Ob odnom svoistve bazisa v prostranstve Banakha”, Zap. matem. ob-va, 4(16), Kharkov, 1940, 106–108 | MR

[4] Smirnov V. I., Kurs vysshei matematiki, t. 5, Gostekhizdat, M., 1947

[5] Ciesielsky Z., “Properties of the orthonormal Franklin system”, Studia Math., 23 (1963), 163–174 | MR

[6] Olevskii A. M., “Ryady Fure nepreryvnykh funktsii po ogranichennym ortonormalnym sistemam”, Izv. AN SSSR. Ser. matem., 30 (1966), 387–432 | MR | Zbl

[7] Shaidukov K. M., “O suschestvovanii ortonormirovannogo bazisa v klasse polinomov”, Nauchn. tr. Kazansk. in-ta inzh.-stroit. neft. promyshlennosti, t. 5, 1957, 119–151

[8] Olevskii A. M., “Ob osobennostyakh tipa Karlemana dlya polnykh ortonormalnykh sistem”, Sib. matem. zh., 8 (1967), 807–826 | MR | Zbl