Geodesic
On properties of an incomplete system of functions close to powerfunctions
Izvestiya. Mathematics , Tome 3 (1969) no. 3, pp. 643-670.

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

On the segment $[0,1]$ we consider a system of functions $\{x^{\lambda_\nu}[1+\varepsilon_\nu(x)]\}$, where the $\varepsilon_\nu(x)$ are small in a definite sense, $\lambda_\nu>0$, $\sum\limits_1^\infty\frac1{\lambda_\nu}\infty$. We study the functions $y(x)$ which are approximated by linear combinations of functions of this system in $L_p(0,1)$ or in $C[0,1]$ . 
@article{IM2_1969_3_3_a8,
     author = {L. A. Leont'eva},
     title = {On properties of an incomplete system of functions close to powerfunctions},
     journal = {Izvestiya. Mathematics },
     pages = {643--670},
     publisher = {mathdoc},
     volume = {3},
     number = {3},
     year = {1969},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1969_3_3_a8/}
}
TY  - JOUR
AU  - L. A. Leont'eva
TI  - On properties of an incomplete system of functions close to powerfunctions
JO  - Izvestiya. Mathematics 
PY  - 1969
SP  - 643
EP  - 670
VL  - 3
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1969_3_3_a8/
LA  - en
ID  - IM2_1969_3_3_a8
ER  - 
%0 Journal Article
%A L. A. Leont'eva
%T On properties of an incomplete system of functions close to powerfunctions
%J Izvestiya. Mathematics 
%D 1969
%P 643-670
%V 3
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1969_3_3_a8/
%G en
%F IM2_1969_3_3_a8
L. A. Leont'eva. On properties of an incomplete system of functions close to powerfunctions. Izvestiya. Mathematics , Tome 3 (1969) no. 3, pp. 643-670. http://geodesic.mathdoc.fr/item/IM2_1969_3_3_a8/

[1] Akhiezer N. I., Lektsii po teorii approksimatsii, Nauka, M., 1965 | MR

[2] Clarkson J. A., Erdös P., “Approximation by polinomials”, Duke Math. J., 10:1 (1943), 5–11 | DOI | MR | Zbl

[3] Schwartz L., Etude des sommes d'exponentielles reeles, Hermann, Paris, 1943 | Zbl

[4] Schwartz L., Etude des sommes d'exponentielles, deuxieme edition, Actualites Scientifiques et Industrielles, 1959

[5] Leonteva L. A., “Ob approksimatsii nepreryvnykh funktsii lineinymi kombinatsiyami posledovatelnykh pervoobraznykh ot odnoi funktsii”, Vestnik Mosk. un-ta. Matematika, mekhanika, 1967, no. 2, 20–29 | MR

[6] Leonteva L. A., “O polnote odnoi sistemy funktsii na otrezke”, Matematicheskie zametki, 4:5 (1968), 557–568 | MR

[7] Gurarii V. I., Matsaev V. I., “Lakunarnye stepennye posledovatelnosti v prostranstvakh $C$ i $L_p$”, Izv. AN SSSR. Ser. matem., 30 (1966), 1–44

[8] Markushevich A. I., Teoriya analiticheskikh funktsii, GITTL, M., L., 1950

[9] Smirnov V. I., Kurs vysshei matematiki, t. IV, GITTL, M., L., 1951