Email this article A Remark on Indicator Functions with Gaps in the Spectrum
- Authors: Kislyakov S.V.1
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Affiliations:
- St. Petersburg Department of Steklov Institute of Mathematics
- Issue: Vol 243, No 6 (2019)
- Pages: 895-899
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/243180
- DOI: https://doi.org/10.1007/s10958-019-04589-z
- ID: 243180
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Abstract
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 χb is fairly thin. A generalization to locally compact Abelian groups is also provided.
About the authors
S. V. Kislyakov
St. Petersburg Department of Steklov Institute of Mathematics
Author for correspondence.
Email: skis@pdmi.ras.ru
Russian Federation, St. Petersburg
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