Geodesic
Series expansion in a system of rational functions
Sbornik. Mathematics, Tome 19 (1973) no. 4, pp. 531-545 
A. M. Lukatskii. Series expansion in a system of rational functions. Sbornik. Mathematics, Tome 19 (1973) no. 4, pp. 531-545. http://geodesic.mathdoc.fr/item/SM_1973_19_4_a2/
@article{SM_1973_19_4_a2,
     author = {A. M. Lukatskii},
     title = {Series expansion in a~system of rational functions},
     journal = {Sbornik. Mathematics},
     pages = {531--545},
     year = {1973},
     volume = {19},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1973_19_4_a2/}
}
TY  - JOUR
AU  - A. M. Lukatskii
TI  - Series expansion in a system of rational functions
JO  - Sbornik. Mathematics
PY  - 1973
SP  - 531
EP  - 545
VL  - 19
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_1973_19_4_a2/
LA  - en
ID  - SM_1973_19_4_a2
ER  - 
%0 Journal Article
%A A. M. Lukatskii
%T Series expansion in a system of rational functions
%J Sbornik. Mathematics
%D 1973
%P 531-545
%V 19
%N 4
%U http://geodesic.mathdoc.fr/item/SM_1973_19_4_a2/
%G en
%F SM_1973_19_4_a2

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

This paper treats the convergence of the Fourier series of a summable function in a system of rational functions on the unit circle, from the inside of the unit circle, and from the outside of the unit circle, for various distributions of the poles of the system. Bibliography: 8 titles.

[1] M. M. Dzhrbashyan, “K teorii ryadov Fure po ratsionalnym funktsiyam”, Izv. AN ArmSSR, seriya fiz.-matem., 9:7 (1956), 3–27 | MR

[2] M. M. Dzhrbashyan, “Razlozhenie po sistemam ratsionalnykh funktsii s fiksirovannymi polyusami”, Izv. AN ArmSSR, seriya fiz.-matem., 2:1 (1967), 3–51 | Zbl

[3] A. A. Kitbalyan, “Razlozheniya po obobschennym trigonometricheskim sistemam”, Izv. AN ArmSSR, seriya fiz.-matem., 16:6 (1963), 3–24 | MR

[4] G. Ts. Tumarkin, “Opisanie klassa funktsii, dopuskayuschikh priblizhenie drobyami s fiksirovannymi polyusami”, Izv. AN ArmSSR, seriya fiz.-matem., 1:2 (1966), 89–105 | MR | Zbl

[5] G. Ts. Tumarkin, “Priblizhenie v razlichnykh metrikakh funktsii, zadannykh na okruzhnosti, posledovatelnostyami ratsionalnykh drobei”, Izv. AN SSR, seriya matem., 30 (1966), 721–766 | MR | Zbl

[6] A. Zigmund, Trigonometricheskie ryady, t. I, izd-vo «Mir», Moskva, 1965 | MR

[7] I. I. Privalov, Granichnye svoistva analiticheskikh funktsii, Gostekhizdat, Moskva, 1960

[8] N. I. Akhiezer, Lektsii po teorii approksimatsii, izd-vo «Nauka», Moskva, 1965 | MR