This article is cited in 1 paper

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

A. V. Tovstolis

Donetsk National University

Abstract: 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.

UDC: 517.5

Received: 06.12.1999
Revised: 09.11.2000

DOI: 10.4213/mzm708

 English version: Mathematical Notes, 2001, 69:6, 853–862

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