A note on one of the Bernstein theorems
Mathematica Bohemica (1993)
- Volume: 118, Issue: 3, page 321-324
- ISSN: 0862-7959
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topBrabec, Jiří. "A note on one of the Bernstein theorems." Mathematica Bohemica 118.3 (1993): 321-324. <http://eudml.org/doc/29084>.
@article{Brabec1993,
abstract = {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.},
author = {Brabec, Jiří},
journal = {Mathematica Bohemica},
keywords = {Bernstein theorems; interpolating operators; Bernstein's inequality; function of exponential type; uniform norm; space of uniformly continuous functions; Bernstein theorems; interpolating operators},
language = {eng},
number = {3},
pages = {321-324},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on one of the Bernstein theorems},
url = {http://eudml.org/doc/29084},
volume = {118},
year = {1993},
}
TY - JOUR
AU - Brabec, Jiří
TI - A note on one of the Bernstein theorems
JO - Mathematica Bohemica
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 118
IS - 3
SP - 321
EP - 324
AB - 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.
LA - eng
KW - Bernstein theorems; interpolating operators; Bernstein's inequality; function of exponential type; uniform norm; space of uniformly continuous functions; Bernstein theorems; interpolating operators
UR - http://eudml.org/doc/29084
ER -
References
top- 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. (1937) Zbl0131.10103
- 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. (1946) Zbl0074.10805
- А. Ф. Тиман, Теория приближения функций действительного переменного, (Theory of approximation of functions of real variable.), Госиздат физмат лит, Moskva, 1960. (1960) Zbl1004.90500
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