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Approximation of Smooth Functions on the Semiaxis by Entire Functions of Bounded Half-Degree

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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.

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  1. Donetsk State University, Ukraine

    A. V. Tovstolis

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  1. A. V. Tovstolis
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Tovstolis, A.V. Approximation of Smooth Functions on the Semiaxis by Entire Functions of Bounded Half-Degree. Mathematical Notes 69, 853–862 (2001). https://doi.org/10.1023/A:1010246902459

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