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arXiv · 1807.02619

On syndetic Riesz sequences

Marcin Bownik·Itay Londner
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Abstract

Applying the solution to the Kadison-Singer problem, we show that every subset $\mathcal{S}$ of the torus of positive Lebesgue measure admits a Riesz sequence of exponentials $\left\{ e^{i\lambda x}\right\} _{\lambda \in \Lambda}$ such that $\Lambda\subset\mathbb{Z}$ is a set with gaps between consecutive elements bounded by ${\displaystyle \frac{C}{\left|\mathcal{S}\right|}}$. In the case when $\mathcal{S}$ is an open set we demonstrate, using quasicrystals, how such $\Lambda$ can be deterministically constructed.

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Marcin Bownik, Itay Londner. 2018-07-07. On syndetic Riesz sequences. https://arxiv.org/abs/1807.02619

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