Sbornik. Mathematics, Tome 15 (1971) no. 3, pp. 415-441
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D. E. Men'shov. Properties of Cesàro means of negative order and of certain other $T$-means for Fourier series of continuous functions. Sbornik. Mathematics, Tome 15 (1971) no. 3, pp. 415-441. http://geodesic.mathdoc.fr/item/SM_1971_15_3_a3/
@article{SM_1971_15_3_a3,
author = {D. E. Men'shov},
title = {Properties of {Ces\`aro} means of negative order and of certain other $T$-means for {Fourier} series of continuous functions},
journal = {Sbornik. Mathematics},
pages = {415--441},
year = {1971},
volume = {15},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1971_15_3_a3/}
}
TY - JOUR
AU - D. E. Men'shov
TI - Properties of Cesàro means of negative order and of certain other $T$-means for Fourier series of continuous functions
JO - Sbornik. Mathematics
PY - 1971
SP - 415
EP - 441
VL - 15
IS - 3
UR - http://geodesic.mathdoc.fr/item/SM_1971_15_3_a3/
LA - en
ID - SM_1971_15_3_a3
ER -
%0 Journal Article
%A D. E. Men'shov
%T Properties of Cesàro means of negative order and of certain other $T$-means for Fourier series of continuous functions
%J Sbornik. Mathematics
%D 1971
%P 415-441
%V 15
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1971_15_3_a3/
%G en
%F SM_1971_15_3_a3
The main result established in this article is the following. Let $\alpha$ be an arbitrary negative nonintegral number. Then every continuous function can be changed on a set of arbitrarily small measure so that if $g(x)$ denotes the new function, then the sequence of the $T$-means (corresponding to the method $(C,\alpha)$) of the function $g(x)$ contains a subsequence converging uniformly to the function $g(x)$. Bibliography: 3 titles.
