A Remark on Indicator Functions with Gaps in the Spectrum

Developing a recent result of F . Nazarov and A . Olevskii, we show that for every subset a in ℝ of finite measure and every ε > 0 there exists b ⊂ ℝ with | b | = | a | and |( b \ a ) ∪ ( a \ b )|≤ ε such that the spectrum of χ b is fairly thin. A generalization to locally compact Abelian groups...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2020-03, Vol.243 (6), p.895-899
Main Author: Kislyakov, S. V.
Format: Article
Language:English
Subjects:
Group theory
Mathematics
Mathematics and Statistics
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Summary:Developing a recent result of F . Nazarov and A . Olevskii, we show that for every subset a in ℝ of finite measure and every ε > 0 there exists b ⊂ ℝ with | b | = | a | and |( b \ a ) ∪ ( a \ b )|≤ ε such that the spectrum of χ b is fairly thin. A generalization to locally compact Abelian groups is also provided.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-019-04589-z