Trigonometric series and self-similar sets

@article{Li2021TrigonometricSA,
  title={Trigonometric series and self-similar sets},
  author={Jialun Li and Tuomas Sahlsten},
  journal={Journal of the European Mathematical Society},
  year={2021}
}
Let $F$ be a self-similar set on $\mathbb{R}$ associated to contractions $f_j(x) = r_j x + b_j$, $j \in \mathcal{A}$, for some finite $\mathcal{A}$, such that $F$ is not a singleton. We prove that if $\log r_i / \log r_j$ is irrational for some $i \neq j$, then $F$ is a set of multiplicity, that is, trigonometric series are not in general unique in the complement of $F$. No separation conditions are assumed on $F$. We establish our result by showing that every self-similar measure $\mu$ on $F… Expand
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