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 
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/
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     title = {Approximation of {Smooth} {Functions} on the {Semiaxis} by {Entire} {Functions} of {Bounded} {Half-Degree}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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