Geodesic
Approximation of Smooth Functions on the Semiaxis by Entire Functions of Bounded Half-Degree
Matematičeskie zametki, Tome 69 (2001) no. 6, pp. 934-943 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we study the pointwise approximation of functions defined on the real semiaxis and having an $r$th derivative bounded almost everywhere. The approximation is performed by means of entire functions of bounded half-degree, which were introduced by S. N. Bernstein. An asymptotically sharp estimate for pointwise approximation of this class of functions is obtained. 
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     title = {Approximation of {Smooth} {Functions} on the {Semiaxis} by {Entire} {Functions} of {Bounded} {Half-Degree}},
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A. V. Tovstolis. Approximation of Smooth Functions on the Semiaxis by Entire Functions of Bounded Half-Degree. Matematičeskie zametki, Tome 69 (2001) no. 6, pp. 934-943. http://geodesic.mathdoc.fr/item/MZM_2001_69_6_a13/

[1] Akhiezer N. I., Lektsii po teorii approksimatsii, Nauka, M., 1965

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

[3] Korneichuk N. P., Tochnye konstanty v teorii priblizheniya, Nauka, M., 1987

[4] Ibragimov I. I., Teoriya priblizheniya tselymi funktsiyami, Elm, Baku, 1979

[5] Bernshtein S. N., “Funktsii konechnoi stepeni i funktsii konechnoi polustepeni”, Sobranie sochinenii, T. 2, AN SSSR, M., 1954, 479–492

[6] Brudnyi Yu. A., “Priblizhenie tselymi funktsiyami na vneshnosti otrezka i poluosi”, Izv. AN SSSR. Ser. matem., 23:4 (1959), 595–612 | MR | Zbl

[7] Nikolskii S. M., “O nailuchshem priblizhenii mnogochlenami funktsii, udovletvoryayuschikh usloviyu Lipshitsa”, Izv. AN SSSR. Ser. matem., 10:4 (1946), 295–322 | MR | Zbl

[8] Korneichuk N. P., Polovina A. I., “O priblizhenii nepreryvnykh differentsiruemykh funktsii algebraicheskimi polinomami na otrezke”, Dokl. AN SSSR, 166:2 (1966), 281–283 | MR

[9] Temlyakov V. N., “Priblizhenie funktsii iz klassa $W^1_\infty $ algebraicheskimi mnogochlenami”, Matem. zametki, 29:4 (1981), 597–602 | MR | Zbl

[10] Trigub R. M., “Pryamye teoremy o priblizhenii algebraicheskimi polinomami gladkikh funktsii na otrezke”, Matem. zametki, 54:6 (1993), 113–121 | MR | Zbl

[11] Bernshtein S. N., “O nailuchshem priblizhenii na vsei veschestvennoi osi pri pomoschi tselykh funktsii dannoi stepeni”, Sobranie sochinenii, T. 2, AN SSSR, M., 1954, 379–383