Geodesic
Estimates for the error of approximation of classes of differentiable functions by Faber–Schauder partial sums
Sbornik. Mathematics, Tome 197 (2006) no. 3, pp. 303-314 
S. B. Vakarchuk; A. N. Shchitov. Estimates for the error of approximation of classes of differentiable functions by Faber–Schauder partial sums. Sbornik. Mathematics, Tome 197 (2006) no. 3, pp. 303-314. http://geodesic.mathdoc.fr/item/SM_2006_197_3_a0/
@article{SM_2006_197_3_a0,
     author = {S. B. Vakarchuk and A. N. Shchitov},
     title = {Estimates for the error of approximation of classes of differentiable functions by {Faber{\textendash}Schauder} partial sums},
     journal = {Sbornik. Mathematics},
     pages = {303--314},
     year = {2006},
     volume = {197},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2006_197_3_a0/}
}
TY  - JOUR
AU  - S. B. Vakarchuk
AU  - A. N. Shchitov
TI  - Estimates for the error of approximation of classes of differentiable functions by Faber–Schauder partial sums
JO  - Sbornik. Mathematics
PY  - 2006
SP  - 303
EP  - 314
VL  - 197
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_2006_197_3_a0/
LA  - en
ID  - SM_2006_197_3_a0
ER  - 
%0 Journal Article
%A S. B. Vakarchuk
%A A. N. Shchitov
%T Estimates for the error of approximation of classes of differentiable functions by Faber–Schauder partial sums
%J Sbornik. Mathematics
%D 2006
%P 303-314
%V 197
%N 3
%U http://geodesic.mathdoc.fr/item/SM_2006_197_3_a0/
%G en
%F SM_2006_197_3_a0

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

In the metric of the space $\varphi(L)$ generated by a continuous even function $\varphi(x)$ increasing on $[0,\infty)$ such that $\varphi(0)=0$, $\lim_{x\to\infty}\varphi(x)=\infty$ one finds estimates of the error of approximation by partial sums of Faber–Schauder series in the function classes $C^1$ and $W^1H_\omega$, where $\omega(t)$ is a concave modulus of continuity. Bibliography: 21 titles.

[1] B. I. Golubov, “O ryadakh Fure nepreryvnykh funktsii po sisteme Khaara”, Izv. AN SSSR. Ser. matem., 28:6 (1964), 1271–1296 | MR | Zbl

[2] G. Faber, “Über die Orthogonalfunktionen des Herrn Haar”, Deutsche Math.-Ver., 19 (1910), 104–112 | Zbl

[3] Z. Ciesielski, “On Haar functions and on the Schauder basis of the space $C_{\langle 0,1\rangle}$”, Bull. Acad. Pol. Sci. Sér. Math. Astron. Phys., 7:4 (1959), 227–232 | MR | Zbl

[4] J. Schauder, “Zur Theorie stetiger Abbildungen in Funktionalräumen”, Math. Z., 26 (1927), 47–65 | DOI | MR | Zbl

[5] V. A. Matveev, “O ryadakh po sisteme Shaudera”, Matem. zametki, 2:3 (1967), 267–278 | MR | Zbl

[6] P. L. Ulyanov, “Predstavlenie funktsii ryadami i klassy $\varphi(L)$”, UMN, 27:2 (1972), 3–52 | MR | Zbl

[7] A. A. Talalyan, “Predstavlenie proizvolnoi izmerimoi funktsii ryadami po funktsiyam sistemy Shaudera”, Izv. AN ArmSSR. Ser. fiz.-matem. nauk, 12:3 (1959), 3–14 | MR

[8] P. L. Ulyanov, “O nekotorykh svoistvakh ryadov po sisteme Shaudera”, Matem. zametki, 7:4 (1970), 431–442 | MR | Zbl

[9] P. L. Ulyanov, “Predstavlenie funktsii klassa $\varphi(L)$ ryadami”, Trudy MIAN, 112, no. 1, 1971, 372–384 | MR | Zbl

[10] P. L. Ulyanov, “Nekotorye voprosy teorii ortogonalnykh i biortogonalnykh ryadov”, Izv. AN AzSSR. Ser. fiz.-tekhn. i matem. nauk, 6 (1965), 11–13 | Zbl

[11] Z. Ciesielski, “Properties of the orthonormal Franklin system”, Studia Math., 23 (1963), 141–157 | MR | Zbl

[12] A. S. Loginov, “Priblizhenie nepreryvnykh funktsii lomanymi”, Matem. zametki, 6:2 (1969), 149–160 | MR | Zbl

[13] I. K. Daugavet, Vvedenie v teoriyu priblizheniya funktsii, LGU, L., 1977 | MR

[14] S. M. Nikolskii, “Ryad Fure funktsii s dannym modulem nepreryvnosti”, Dokl. AN SSSR, 52:3 (1946), 191–194 | MR

[15] S. B. Vakarchuk, A. N. Schitov, “Nekotorye voprosy priblizheniya chastnymi summami ryadov Fabera–Shaudera v metrike prostranstva $\varphi(L)$”, Izv. vuzov. Ser. matem., 2004, no. 10, 82–85 | MR | Zbl

[16] A. N. Schitov, S. B. Vakarchuk, “O priblizhenii funktsii polinomami po sisteme Khaara i chastnymi summami ryadov po sisteme Fabera–Shaudera”, Tezisy dokladov mezhdunarodnoi konferentsii pamyati V. Ya. Bunyakovskogo (1804–1889), In-t matematiki NAN Ukrainy, Kiev, 2004, 136–137

[17] N. P. Korneichuk, Tochnye konstanty v teorii priblizheniya, Nauka, M., 1987 | MR

[18] I. M. Sobol, Kvadraturnye formuly i funktsii Khaara, Nauka, M., 1969 | MR

[19] N. P. Khoroshko, “O nailuchshem priblizhenii v metrike $L$ nekotorykh klassov funktsii polinomami po sisteme Khaara”, Matem. zametki, 6:1 (1969), 47–54 | MR | Zbl

[20] N. P. Korneichuk, Splainy v teorii priblizheniya, Nauka, M., 1984 | MR

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