Geodesic
On the question of the asymptotic behavior of best approximations of continuous functions
Sbornik. Mathematics, Tome 38 (1981) no. 3, pp. 365-380 Cet article a éte moissonné depuis la source Math-Net.Ru

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For classes of functions with a given majorant of the modulus of continuity of the rth derivative, functions are constructed whose best approximations by trigonometric polynomials behave in the same way on a certain subsequence of indices as the suprema of the corresponding best approximations on these classes. Bibliography: 6 titles. 
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V. N. Temlyakov. On the question of the asymptotic behavior of best approximations of continuous functions. Sbornik. Mathematics, Tome 38 (1981) no. 3, pp. 365-380. http://geodesic.mathdoc.fr/item/SM_1981_38_3_a2/

[1] K. I. Babenko, “O nailuchshikh priblizheniyakh odnogo klassa analiticheskikh funktsii”, Izv. AN SSSR, seriya matem., 22 (1958), 631–640 | MR | Zbl

[2] N. P. Korneichuk, Ekstremalnye zadachi teorii priblizheniya, izd-vo “Nauka”, Moskva, 1976 | MR

[3] S. M. Nikolskii, “Ob interpolirovanii i nailuchshem priblizhenii differentsiruemykh periodicheskikh funktsii trigonometricheskimi polinomami”, Izv. AN SSSR, seriya matem., 10 (1946), 393–410

[4] S. M. Nikolskii, “Priblizhenie funktsii trigonometricheskimi polinomami v srednem”, Izv. AN SSSR, seriya matem., 10 (1946), 207–256

[5] V. N. Temlyakov, “Ob asimptoticheskom povedenii nailuchshikh priblizhenii nepreryvnykh funktsii”, DAN SSSR, 228:2 (1976), 318–321 | MR | Zbl

[6] V. N. Temlyakov, “Asimptoticheskoe povedenie nailuchshikh priblizhenii nepreryvnykh funktsii”, Izv. AN SSSR, seriya matem., 41 (1977), 587–606