Geodesic
Approximation of functions of bounded $p$-variation by polynomials in terms of the Faber–Schauder system
Matematičeskie zametki, Tome 62 (1997) no. 3, pp. 363-371 
S. S. Volosivets. Approximation of functions of bounded $p$-variation by polynomials in terms of the Faber–Schauder system. Matematičeskie zametki, Tome 62 (1997) no. 3, pp. 363-371. http://geodesic.mathdoc.fr/item/MZM_1997_62_3_a4/
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     author = {S. S. Volosivets},
     title = {Approximation of functions of bounded $p$-variation by polynomials in terms of the {Faber{\textendash}Schauder} system},
     journal = {Matemati\v{c}eskie zametki},
     pages = {363--371},
     year = {1997},
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     url = {http://geodesic.mathdoc.fr/item/MZM_1997_62_3_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper the best polynomial approximation in terms of the system of Faber–Schauder functions in the space $C_p[0,1]$ is studied. The constant in the estimate of Jackson's inequality for the best approximation in the metric of $C_p[0,1]$ and the estimate of the modulus of continuity $\omega_{1-1/p}$ are refined.

[1] Kashin B. S., Saakyan A. A., Ortogonalnye ryady, Nauka, M., 1984 | Zbl

[2] Terekhin A. P., “Priblizhenie funktsii ogranichennoi $p$-variatsii”, Izv. vuzov. Matem., 1965, no. 2, 171–187 | MR | Zbl

[3] Terekhin A. P., “Funktsii ogranichennoi $p$-variatsii s dannym poryadkom modulya nepreryvnosti”, Matem. zametki, 12:5 (1972), 523–530 | MR | Zbl

[4] Golubov B. I., Efimov A. V., Skvortsov V. A., Ryady i preobrazovaniya Uolsha, Nauka, M., 1987 | Zbl

[5] Golubov B. I., “Kriterii kompaktnosti mnozhestv v prostranstvakh funktsii obobschennoi ogranichennoi variatsii”, Izv. AN ArmSSR, 3:6 (1968), 409–416 | MR | Zbl

[6] Volosivets S. S., “Priblizhenie funktsii ogranichennoi $p$-variatsii polinomami po sistemam Khaara i Uolsha”, Matem. zametki, 53:6 (1993), 11–21 | MR | Zbl

[7] Ciesielski Z., “Some properties of Schauder basis of the space $C_{\langle0,1\rangle}$”, Bull. Acad. Polon. Sci., 8:3 (1960), 141–144 | MR | Zbl

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

[9] Volosivets S. S., “Priblizhenie funktsii ogranichennoi $p$-fluktuatsii polinomami po multiplikativnym sistemam”, Anal. Math., 21:1 (1995), 61–77 | DOI | MR | Zbl

[10] Stechkin S. B., “Ob absolyutnoi skhodimosti ryadov Fure, II”, Izv. AN SSSR. Ser. matem., 19:4 (1955), 221–246 | MR | Zbl

[11] Konyushkov A. A., “O skhodimosti nekotorykh ryadov iz koeffitsientov Fure”, UMN, 14:1 (1959), 189–196 | MR

[12] Goryachev A. P., “O koeffitsientakh Fure po sisteme Fabera–Shaudera”, Matem. zametki, 15:2 (1974), 341–352 | MR | Zbl