Matematičeskie zametki, Tome 20 (1976) no. 1, pp. 69-78
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N. T. Anisimova. Divergent Fourier series with respect to orthonormalized systems of smooth functions. Matematičeskie zametki, Tome 20 (1976) no. 1, pp. 69-78. http://geodesic.mathdoc.fr/item/MZM_1976_20_1_a7/
@article{MZM_1976_20_1_a7,
author = {N. T. Anisimova},
title = {Divergent {Fourier} series with respect to orthonormalized systems of smooth functions},
journal = {Matemati\v{c}eskie zametki},
pages = {69--78},
year = {1976},
volume = {20},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_1_a7/}
}
TY - JOUR
AU - N. T. Anisimova
TI - Divergent Fourier series with respect to orthonormalized systems of smooth functions
JO - Matematičeskie zametki
PY - 1976
SP - 69
EP - 78
VL - 20
IS - 1
UR - http://geodesic.mathdoc.fr/item/MZM_1976_20_1_a7/
LA - ru
ID - MZM_1976_20_1_a7
ER -
%0 Journal Article
%A N. T. Anisimova
%T Divergent Fourier series with respect to orthonormalized systems of smooth functions
%J Matematičeskie zametki
%D 1976
%P 69-78
%V 20
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_1976_20_1_a7/
%G ru
%F MZM_1976_20_1_a7
In this paper it is proved that for any function $f\in L^2[-\pi;\pi]$, $\|f\|_2>0$, there exists a complete orthonormalized system of uniformly bounded trigonometric polynomials with respect to which the Fourier series of this function is divergent almost everywhere in the interval $[-\pi;\pi]$.
