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Indicator functions with uniformly bounded Fourier sums and large gaps in the spectrum

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S. V. Kislyakov, P. S. Perstneva

Classical Analysis and ODEs · Submitted 3 Jun 2020

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Indicator functions mentioned in the title are constructed on an arbitrary nondiscrete locally compact Abelian group of finite dimension.

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arXiv ID2006.02561 (version 1)
Pith IDVSKXYL6Y, Pith's permanent record of this paper and its review
CitationP. S. Perstneva, S. V. Kislyakov. "Indicator functions with uniformly bounded Fourier sums and large gaps in the spectrum." arXiv:2006.02561 (2020). https://pith.science/paper/VSKXYL6Y
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,090 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.58 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.21 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

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 Men$'$shov-type correction theorem.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Indicator functions mentioned in the title are constructed on an arbitrary nondiscrete locally compact Abelian group of finite dimension. contribution 0.85 0.83 0.19 asserted 1.00
s1 Moreover, they can be obtained by small perturbation from any indicator function fixed beforehand. result 0.79 0.84 0.15 hedged possibility 0.64
s2 In the case of a noncompact group, the term "Fourier sums" should be understood as "partial Fourier integrals". interpretation 0.79 0.30 0.05 asserted 0.99
s3 A certain weighted version of the result is also provided. contribution 0.76 0.87 0.07 asserted 0.99
s4 This version leads to a new Men$'$shov-type correction theorem. result 0.58 0.87 0.21 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original 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 Men$'$shov-type correction theorem.

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