Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 38, Tome 376 (2010), pp. 25-47
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P. Ivanishvili; S. V. Kislyakov. Correction up to a function with sparse spectrum and uniformly convergent Fourier series. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 38, Tome 376 (2010), pp. 25-47. http://geodesic.mathdoc.fr/item/ZNSL_2010_376_a1/
@article{ZNSL_2010_376_a1,
author = {P. Ivanishvili and S. V. Kislyakov},
title = {Correction up to a~function with sparse spectrum and uniformly convergent {Fourier} series},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {25--47},
year = {2010},
volume = {376},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_376_a1/}
}
TY - JOUR
AU - P. Ivanishvili
AU - S. V. Kislyakov
TI - Correction up to a function with sparse spectrum and uniformly convergent Fourier series
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2010
SP - 25
EP - 47
VL - 376
UR - http://geodesic.mathdoc.fr/item/ZNSL_2010_376_a1/
LA - ru
ID - ZNSL_2010_376_a1
ER -
%0 Journal Article
%A P. Ivanishvili
%A S. V. Kislyakov
%T Correction up to a function with sparse spectrum and uniformly convergent Fourier series
%J Zapiski Nauchnykh Seminarov POMI
%D 2010
%P 25-47
%V 376
%U http://geodesic.mathdoc.fr/item/ZNSL_2010_376_a1/
%G ru
%F ZNSL_2010_376_a1
In 1984, the second author proved that, after correction on a set of arbitrarily small measure, any continuous function on a finite-dimensional compact Abelian group acquires sparse spectrum and uniformly convergent Fourier series. In the present paper we refine the result in two directions: first, we ensure uniform convergence in a stronger sense; second, we prove that the spectrum after correction can be put in even more peculiar sparse sets. Bibl. – 6 titles.
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