Approximation of Functions of Dirichlet Class by Fej\'er Means
Matematičeskie zametki, Tome 81 (2007) no. 5, pp. 744-750.

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

For the Dirichlet classes $\mathscr D_p$ of holomorphic functions in the disk, we obtain the exact orders of best polynomial approximations and of upper bounds for deviations of Fejér means of Taylor series in the Hardy spaces $H_p$.
Keywords: Dirichlet class of holomorphic functions, Fejér mean, best polynomial approximation, Taylor series, Hardy space, Fubini theorem, Riesz theorem.
@article{MZM_2007_81_5_a11,
     author = {V. V. Savchuk},
     title = {Approximation of {Functions} of {Dirichlet} {Class} by {Fej\'er} {Means}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {744--750},
     publisher = {mathdoc},
     volume = {81},
     number = {5},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_5_a11/}
}
TY  - JOUR
AU  - V. V. Savchuk
TI  - Approximation of Functions of Dirichlet Class by Fej\'er Means
JO  - Matematičeskie zametki
PY  - 2007
SP  - 744
EP  - 750
VL  - 81
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_81_5_a11/
LA  - ru
ID  - MZM_2007_81_5_a11
ER  - 
%0 Journal Article
%A V. V. Savchuk
%T Approximation of Functions of Dirichlet Class by Fej\'er Means
%J Matematičeskie zametki
%D 2007
%P 744-750
%V 81
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2007_81_5_a11/
%G ru
%F MZM_2007_81_5_a11
V. V. Savchuk. Approximation of Functions of Dirichlet Class by Fej\'er Means. Matematičeskie zametki, Tome 81 (2007) no. 5, pp. 744-750. http://geodesic.mathdoc.fr/item/MZM_2007_81_5_a11/

[1] Dzh. Garnett, Ogranichennye analiticheskie funktsii, Mir, M., 1984 | MR | Zbl

[2] A. I. Stepanets, Ravnomernye priblizheniya trigonometricheskimi polinomami, Lineinye metody, Naukova dumka, Kiev, 1981 | MR | Zbl

[3] G. Alexits, “Sur l'ordre de grandeur de l'approximation d'une fonction par les moyennes de sa série de Fourier”, Mat. Fiz. Lapok., 48 (1941), 410–422 | MR | Zbl

[4] A. Zygmund, “On the degree of approximation of functions by Fejer means”, Bull. Amer. Math. Soc., 51 (1945), 274–278 | DOI | MR | Zbl

[5] S. B. Stechkin, “Otsenka ostatka ryada Teilora dlya nekotorykh klassov analiticheskikh funktsii”, Izv. AN SSSR. Ser. matem., 17:5 (1953), 461–472 | MR | Zbl

[6] E. A. Storozhenko, “Priblizhenie funktsii klassa $H^p$, $0

\le1$”, Matem. sb., 105:4 (1978), 601–621 | MR | Zbl

[7] A. Pinkus, $n$-Widths in Approximation Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3, Springer-Verlag, Berlin, 1985 | MR | Zbl

[8] K. I. Babenko, “Nailuchshie priblizheniya klassov analiticheskikh funktsii”, Izv. AN SSSR. Ser. matem., 22:5 (1958), 631–640 | MR | Zbl

[9] L. V. Taikov, “O nailuchshem priblizhenii v srednem nekotorykh klassov analiticheskikh funktsii”, Matem. zametki, 1:2 (1967), 155–162 | MR | Zbl

[10] G. Soares de Souza, G. Sampson, “A function in the Dirichlet space such that its Fourier series diverges almost everywhere”, Proc. Amer. Math. Soc., 120:3 (1994), 723–726 | DOI | MR | Zbl

[11] N. P. Korneichuk, Ekstremalnye zadachi teorii priblizheniya, Nauka, M., 1976 | MR