TY - JOUR

T1 - A Remark on Indicator Functions with Gaps in the Spectrum

AU - Kislyakov, S. V.

N1 - Publisher Copyright: © 2019, Springer Science+Business Media, LLC, part of Springer Nature. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2019/12/1

Y1 - 2019/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85075043074&partnerID=8YFLogxK

U2 - 10.1007/s10958-019-04589-z

DO - 10.1007/s10958-019-04589-z

M3 - Article

AN - SCOPUS:85075043074

VL - 243

SP - 895

EP - 899

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -