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Title: A note on one of the Bernstein theorems (English)
Author: Brabec, Jiří
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 118
Issue: 3
Year: 1993
Pages: 321-324
Summary lang: English
Category: math
Summary: One of the Bernstein theorems that the class of bounded functions of the exponential type is dense in the space of bounded and uniformly continuous functions. This theorem follows from a convergence theorem for some interpolating operators on the real axis. (English)
Keyword: Bernstein theorems
Keyword: interpolating operators
Keyword: Bernstein's inequality
Keyword: function of exponential type
Keyword: uniform norm
Keyword: space of uniformly continuous functions
MSC: 30D10
MSC: 41A05
MSC: 41A36
idZBL: Zbl 0783.41001
idMR: MR1239126
DOI: 10.21136/MB.1993.125930
Date available: 2009-09-24T21:00:41Z
Last updated: 2020-07-29
Stable URL:
Reference: [1] С. H. Бернштейн: Экстремальные свойства полиномов и наилучшее приближение непрерывных функций одной вещственной переменной.(Extremal properties of polynomials and the best approximations of continuous functions of one real variable.), Гонти, 1937. Zbl 0131.10103
Reference: [2] С. H. Бернштейн: О наилучшем приближении непрерывных функций на всей вещественной оси при помощи целых функций данной степени I.(On the best approximation of continuous functions on the whole real axis in terms of entire functions of a given degree I.) Сочинения, т. II, 1946. Zbl 0074.10805
Reference: [3] А. Ф. Тиман: Теория приближения функций действительного переменного.(Theory of approximation of functions of real variable.), Госиздат физмат лит, Moskva, 1960. Zbl 1004.90500


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