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Countable unions of intervals without Riesz spectra
Abstract
We prove that every set S = ⋃n ≥ 0 [ t2 n + 1 , t2 n ), where t0 > t1 > ⋯ > 0 and tn → 0, admits no Riesz spectrum. This extends the result of Kozma, Nitzan, and Olevskii \cite{KNO} to a wide class of countable unions of intervals.
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BibTeX
@misc{lee2026countable,
title = {{Countable unions of intervals without Riesz spectra}},
author = {Dae Gwan Lee},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40400},
eprint = {2610.40400},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40400},
}
RIS
TY - UNPB
TI - Countable unions of intervals without Riesz spectra
AU - Dae Gwan Lee
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40400
UR - https://arxiv.org/abs/2610.40400
AB - We prove that every set S = ⋃_n ≥ 0 [ t_2 n + 1 , t_2 n ), where t_0 > t_1 > ⋯ > 0 and t_n → 0, admits no Riesz spectrum. This extends the result of Kozma, Nitzan, and Olevskii \cite{KNO} to a wide class of countable unions of intervals.
ER -