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arXiv · 2112.08680

Completeness of Discrete Translates in $H^1(\mathbb{R})$

Bhawna Dharra·S. Sivananthan
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Abstract

We provide a characterization of discrete sets $\Lambda \subset \mathbb{R}$ that admit a function whose $\Lambda$-translates are complete in the Hardy space $H^1(\mathbb{R})$. In particular, we show that such a set cannot be uniformly discrete. We then give a uniformly discrete $\Lambda \subset \mathbb{R}$ which admits a pair of functions such that their $\Lambda$-translates are complete in $H^1(\mathbb{R})$.

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Bhawna Dharra, S. Sivananthan. 2021-12-16. Completeness of Discrete Translates in $H^1(\mathbb{R})$. https://doi.org/10.1090/proc%2F16070

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