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Approximation of Smooth Functions on the Semiaxis by Entire Functions of Bounded Half-Degree
Authors:Tovstolis  A. V.
Affiliation:(1) Donetsk State University, Ukraine
Abstract:
In this paper, we study the pointwise approximation of functions defined on the real semiaxis and having an rth 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.
Keywords:approximation of smooth functions  entire function of bounded half-degree  Euler ideal spline
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