On the Annihilation of Thin Sets

Tomer Amit; Alexander Olevskii

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arXiv · 1711.04131

On the Annihilation of Thin Sets

Tomer Amit·Alexander Olevskii

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Abstract

One says that a pair of sets $(S,Q)$ in $\mathbb{R}$ is 'annihilating' if no function can be concentrated on $S$ while having its Fourier transform concentrated on $Q$. One uses to distinguish between weak and strong annihilation types. It is well known that if both sets $S$ and $Q$ are of finite measure then they are strongly annihilating. In this paper we prove that if $S$ is a set of finite measure with periodic gaps, and $Q$ is a set of density zero, then weak annihilation holds. On the other hand a counter-example is constructed, showing that strong annihilation, in general, does not.

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BibTeX RIS

Tomer Amit, Alexander Olevskii. 2017-11-11. On the Annihilation of Thin Sets. https://arxiv.org/abs/1711.04131

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