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arXiv · 2603.08482

Asymmetric uniqueness sets in $\ell^q$

Adem Limani·Tomas Persson
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Abstract

We exhibit an asymmetry phenomenon for uniqueness sets in $\ell^q$. Specifically, we construct sets that do not support measures with $\ell^q$-summable Fourier coefficients, yet simultaneously support measures whose positive frequencies decay faster than polynomials. In the language of Fourier uniqueness, this highlights a striking divergence between the unilateral and bilateral $\ell^q$ uniqueness problems.

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Adem Limani, Tomas Persson. 2026-03-09. Asymmetric uniqueness sets in $\ell^q$. https://arxiv.org/abs/2603.08482

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