Luzin's Correction Theorem and the Coefficients of Fourier Expansions in the Faber--Schauder System
Matematičeskie zametki, Tome 93 (2013) no. 2, pp. 172-178
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Suppose that $b_n\downarrow0$ and $\sum_{n=1}^{\infty}({b_n}/{n})=+\infty$. In this paper, it is proved that any measurable almost everywhere finite function on $[0,1]$ can be corrected on a set of arbitrarily small measure to a continuous function $\widetilde{f}$ so that the nonzero moduli $|A_n(\widetilde{f}\mspace{4mu})|$ of the Fourier–Faber–Schauder coefficients of the corrected function are $b_n$.
Keywords:
Luzin's correction theorem, Faber–Schauder system, correcting function, Faber–Schauder spectrum.
@article{MZM_2013_93_2_a1,
author = {M. G. Grigoryan and V. G. Krotov},
title = {Luzin's {Correction} {Theorem} and the {Coefficients} of {Fourier} {Expansions} in the {Faber--Schauder} {System}},
journal = {Matemati\v{c}eskie zametki},
pages = {172--178},
publisher = {mathdoc},
volume = {93},
number = {2},
year = {2013},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_2_a1/}
}
TY - JOUR AU - M. G. Grigoryan AU - V. G. Krotov TI - Luzin's Correction Theorem and the Coefficients of Fourier Expansions in the Faber--Schauder System JO - Matematičeskie zametki PY - 2013 SP - 172 EP - 178 VL - 93 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MZM_2013_93_2_a1/ LA - ru ID - MZM_2013_93_2_a1 ER -
%0 Journal Article %A M. G. Grigoryan %A V. G. Krotov %T Luzin's Correction Theorem and the Coefficients of Fourier Expansions in the Faber--Schauder System %J Matematičeskie zametki %D 2013 %P 172-178 %V 93 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/MZM_2013_93_2_a1/ %G ru %F MZM_2013_93_2_a1
M. G. Grigoryan; V. G. Krotov. Luzin's Correction Theorem and the Coefficients of Fourier Expansions in the Faber--Schauder System. Matematičeskie zametki, Tome 93 (2013) no. 2, pp. 172-178. http://geodesic.mathdoc.fr/item/MZM_2013_93_2_a1/