Indicator functions with uniformly bounded Fourier sums and large gaps in the spectrum
Classical Analysis and ODEs
2020-06-05 v1
Abstract
Indicator functions mentioned in the title are constructed on an arbitrary nondiscrete locally compact Abelian group of finite dimension. Moreover, they can be obtained by small perturbation from any indicator function fixed beforehand. In the case of a noncompact group, the term "Fourier sums" should be understood as "partial Fourier integrals". A certain weighted version of the result is also provided. This version leads to a new Menshov-type correction theorem.
Keywords
Cite
@article{arxiv.2006.02561,
title = {Indicator functions with uniformly bounded Fourier sums and large gaps in the spectrum},
author = {S. V. Kislyakov and P. S. Perstneva},
journal= {arXiv preprint arXiv:2006.02561},
year = {2020}
}