Geodesic
Approximating one class of finitely differentiable functions by another
Izvestiya. Mathematics, Tome 61 (1997) no. 2, pp. 347-362 
S. N. Kudryavtsev. Approximating one class of finitely differentiable functions by another. Izvestiya. Mathematics, Tome 61 (1997) no. 2, pp. 347-362. http://geodesic.mathdoc.fr/item/IM2_1997_61_2_a5/
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     title = {Approximating one class of finitely differentiable functions by another},
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     url = {http://geodesic.mathdoc.fr/item/IM2_1997_61_2_a5/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Necessary and sufficient conditions are found for approximating (with preassigned accuracy in an integral metric) a class of functions with a given majorant for the moduli of continuity of the highest derivatives by another class.

[1] Timan A. F., “Deformatsiya metricheskikh prostranstv i nekotorye svyazannye s nei voprosy teorii funktsii”, UMN, 20:2 (1965), 53–87 | MR | Zbl

[2] Korneichuk N. P., “Neravenstva dlya differentsiruemykh periodicheskikh funktsii i nailuchshee priblizhenie odnogo klassa funktsii drugim”, Izv. AN SSSR. Ser. matem., 36:2 (1972), 423–434 | MR

[3] Arestov V. V., Gabushin V. N., “O priblizhenii klassov differentsiruemykh funktsii”, Matem. zametki, 9:2 (1971), 105–112 | MR | Zbl

[4] Subbotin Yu. N., “Svyaz splain-priblizhenii s zadachei priblizheniya klassa klassom”, Matem. zametki, 9:5 (1971), 501–510 | MR | Zbl

[5] Kudryavtsev S. N., “Nekotorye zadachi teorii priblizhenii dlya odnogo klassa funktsii konechnoi gladkosti”, Matem. sb., 183:2 (1992), 3–20

[6] Kudryavtsev S. N., “Vosstanovlenie funktsii vmeste s ikh proizvodnymi po znacheniyam funktsii v zadannom chisle tochek”, Izv. AN. Ser. matem., 58:6 (1994), 79–104 | MR | Zbl