Approximation Properties of Poisson Integrals for the Classes~$C^{\psi}_{\beta}H^{\alpha}$
Matematičeskie zametki, Tome 96 (2014) no. 6, pp. 939-952.

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

Questions dealing with the approximation of functions from the classes $C^{\psi}_{\beta}H^{\alpha}$ by Poisson integrals are studied. The Kolmogorov–Nikolskii problem for Poisson integrals for the classes $C^{\psi}_{\beta}H^{\alpha}$ is solved in the uniform metric.
Keywords: approximation of functions, the classes $C^{\psi}_{\beta}H^{\alpha}$, Fourier series, Kolmogorov–Nikolskii problem, $(\psi,\beta)$-derivative.
Mots-clés : Poisson integral
@article{MZM_2014_96_6_a13,
     author = {Yu. I. Kharkevich and T. A. Stepanyuk},
     title = {Approximation {Properties} of {Poisson} {Integrals} for the {Classes~}$C^{\psi}_{\beta}H^{\alpha}$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {939--952},
     publisher = {mathdoc},
     volume = {96},
     number = {6},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_6_a13/}
}
TY  - JOUR
AU  - Yu. I. Kharkevich
AU  - T. A. Stepanyuk
TI  - Approximation Properties of Poisson Integrals for the Classes~$C^{\psi}_{\beta}H^{\alpha}$
JO  - Matematičeskie zametki
PY  - 2014
SP  - 939
EP  - 952
VL  - 96
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2014_96_6_a13/
LA  - ru
ID  - MZM_2014_96_6_a13
ER  - 
%0 Journal Article
%A Yu. I. Kharkevich
%A T. A. Stepanyuk
%T Approximation Properties of Poisson Integrals for the Classes~$C^{\psi}_{\beta}H^{\alpha}$
%J Matematičeskie zametki
%D 2014
%P 939-952
%V 96
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2014_96_6_a13/
%G ru
%F MZM_2014_96_6_a13
Yu. I. Kharkevich; T. A. Stepanyuk. Approximation Properties of Poisson Integrals for the Classes~$C^{\psi}_{\beta}H^{\alpha}$. Matematičeskie zametki, Tome 96 (2014) no. 6, pp. 939-952. http://geodesic.mathdoc.fr/item/MZM_2014_96_6_a13/

[1] A. I. Stepanets, Klassifikatsiya i priblizhenie periodicheskikh funktsii, Naukova dumka, Kiev, 1987 | MR | Zbl

[2] A. I. Stepanets, Metody teorii priblizhenii. I, Tr. In-ta matem. NAN Ukrainy, 40, In-t matem. NAN Ukrainy, Kiev, 2002 | MR | Zbl

[3] V. A. Baskakov, “O nekotorykh svoistvakh operatorov tipa operatorov Abelya–Puassona”, Matem. zametki, 17:2 (1975), 169–180 | MR | Zbl

[4] S. M. Nikolskii, “Asimptoticheskaya otsenka ostatka pri priblizhenii summami Fure”, Dokl. AN SSSR, 32:6 (1941), 386–389 | MR | Zbl

[5] S. M. Nikolskii, “Priblizhenie periodicheskikh funktsii trigonometricheskimi mnogochlenami”, Tr. Matem. in-ta im. V. A. Steklova, 15, Izd-vo AN SSSR, M.–L., 1945, 3–76 | MR | Zbl

[6] B. Nagy, “Sur une classe générale de procédés de sommation pour les séries de Fourier”, Hung. Acta Math., 1 (1948), 14–52 | Zbl

[7] A. F. Timan, “Approksimativnye svoistva lineinykh metodov summirovaniya ryadov Fure”, Izv. AN SSSR. Ser. matem., 17:2 (1953), 99–134 | MR | Zbl

[8] A. F. Timan, Teoriya priblizheniya funktsii deistvitelnogo peremennogo, Fizmatgiz, M., 1960

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

[10] V. T. Gavrilyuk, A. I. Stepanets, “Priblizhenie differentsiruemykh funktsii polinomami Rogozinskogo”, Ukr. matem. zhurn., 25:1 (1973), 3–13 | Zbl

[11] A. V. Efimov, “Lineinye metody priblizheniya nekotorykh klassov nepreryvnykh periodicheskikh funktsii”, Sbornik rabot po lineinym metodam summirovaniya ryadov Fure, Tr. MIAN SSSR, 62, Izd-vo AN SSSR, M., 1961, 3–47 | MR | Zbl

[12] A. S. Serdyuk, E. Yu. Ovsii, “Approximation of the classes $C^{\psi}_{\beta}H_\omega$ by generalized Zygmund sums”, Ukrainian Math. J., 61:4 (2009), 627–644 | DOI | MR | Zbl

[13] E. Yu. Ovsii, “Nablizhennya klasiv $C^{\psi}_{\beta}H_\omega$ uzagalnenimi trigonometrichnimi polinomami”, Preprint NAN Ukraïni, In-t matematiki NAN Ukraïni, Kiïv, 2009

[14] L. I. Bausov, “Lineinye metody summirovaniya ryadov Fure s zadannymi pryamougolnymi matritsami, II”, Izv. vuzov. Matem., 1966, no. 6, 3–17 | MR | Zbl

[15] T. V. Zhyhallo, Yu. I. Kharkevych, “Approximation of $(\psi,\beta)$-differentiable functions by Poisson integrals in the uniform metric”, Ukrainian Math. J., 61:11 (2009), 1757–1779 | DOI | MR

[16] T. V. Zhyhallo, Yu. I. Kharkevych, “Approximation of functions from the class $C^{\psi}_{\beta\infty}$ by Poisson integrals in the uniform metric”, Ukrainian Math. J., 61:12 (2009), 1893–1914 | DOI | MR | Zbl