Uniqueness sets of positive measure for the trigonometric system

There exists a family $\mathcal{B}$ of one-to-one mappings $B \colon \mathbb{Z}\to\mathbb{Z}$ satisfying the condition $B(-n) \equiv -B(n)$ such that for each $B \in \mathcal{B}$ there exists a perfect uniqueness set of positive measure for the $B$-rearranged trigonometric system $\{\exp(iB(n)x)\}$....

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Bibliographic Details
Published in:Izvestiya. Mathematics 2022, Vol.86 (6), p.1179-1203
Main Author: Plotnikov, Mikhail Gennadevich
Format: Article
Language:English
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Summary:There exists a family $\mathcal{B}$ of one-to-one mappings $B \colon \mathbb{Z}\to\mathbb{Z}$ satisfying the condition $B(-n) \equiv -B(n)$ such that for each $B \in \mathcal{B}$ there exists a perfect uniqueness set of positive measure for the $B$-rearranged trigonometric system $\{\exp(iB(n)x)\}$. For a certain wider class of rearrangements of the trigonometric system, the strengthened assertion holds from the Stechkin-Ul'yanov conjecture.
ISSN:1064-5632
1468-4810
DOI:10.4213/im9263e