Geodesic
Uniform polynomial approximation of entire functions on arbitrary compact sets in the complex plane
Matematičeskie zametki, Tome 58 (1995) no. 3, pp. 355-364.

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

For an arbitrary compact set $K\subset\mathbb C$, we relate the order and the type of an entire function $f$ to the sequence $E_n(f,H)$ of best polynomial approximations to this function on $K$. 
@article{MZM_1995_58_3_a3,
     author = {A. A. Dovgoshey},
     title = {Uniform polynomial approximation of entire functions on arbitrary compact sets in the complex plane},
     journal = {Matemati\v{c}eskie zametki},
     pages = {355--364},
     publisher = {mathdoc},
     volume = {58},
     number = {3},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1995_58_3_a3/}
}
TY  - JOUR
AU  - A. A. Dovgoshey
TI  - Uniform polynomial approximation of entire functions on arbitrary compact sets in the complex plane
JO  - Matematičeskie zametki
PY  - 1995
SP  - 355
EP  - 364
VL  - 58
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1995_58_3_a3/
LA  - ru
ID  - MZM_1995_58_3_a3
ER  - 
%0 Journal Article
%A A. A. Dovgoshey
%T Uniform polynomial approximation of entire functions on arbitrary compact sets in the complex plane
%J Matematičeskie zametki
%D 1995
%P 355-364
%V 58
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1995_58_3_a3/
%G ru
%F MZM_1995_58_3_a3
A. A. Dovgoshey. Uniform polynomial approximation of entire functions on arbitrary compact sets in the complex plane. Matematičeskie zametki, Tome 58 (1995) no. 3, pp. 355-364. http://geodesic.mathdoc.fr/item/MZM_1995_58_3_a3/

[1] Bernshtein S. N., “O nailuchshem priblizhenii nepreryvnykh funktsii posredstvom mnogochlenov dannoi stepeni (1912)”, Sobranie sochinenii, T. 1, Izd-vo AN SSSR, M., 1952, 11–104

[2] Walsh I. L., “Uber den grad der Approximation einer analytishen funktion”, Minchner Bericte, 1926, 223–229

[3] Batyrev A. V., “K voprosu o nailuchshem priblizhenii analiticheskoi funktsii polinomami”, DAN SSSR, 76 (1951), 173–175 | MR | Zbl

[4] Reddy A. R., “A contribution to Best Approximation in the $L^2$ Norm”, J. Approx. Theory, 11:1 (1974), 110–117 | DOI | MR | Zbl

[5] Ibragimov I. I., Shikhaliev N. I., “O nailuchshem priblizhenii v srednem analiticheskikh funktsii v prostranstve $L_p$”, Tr. IMM AN Azerb. SSR, 1977, 84–96 | Zbl

[6] Giroux A., “Approximation of Entire Functions over Bounded Domains”, J. Approx. Theory, 28:1 (1980), 45–53 | DOI | MR | Zbl

[7] Vakarchuk S. B., “O nailuchshem polinomialnom priblizhenii analiticheskikh v edinichnom kruge funktsii”, Ukr. matem. zhurn., 42:6 (1990), 838–843 | MR

[8] Muradov V. M., “O nailuchshem polinomialnom priblizhenii analiticheskikh funktsii mnogikh kompleksnykh peremennykh”, DAN AzSSR, 1984, no. 3, 11–14 | MR | Zbl

[9] Goluzin G. M., Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966