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arXiv · 2611.03334

A counterexample concerning weighted convolution on the integers

Frédéric Morneau-Guérin·Thomas Ransford
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Abstract

Let $1<p<\infty$ and let $w:\mathbb{Z}\to(0,\infty)$ be a weight. When is the weighted space $\ell^p(\mathbb{Z},w)$ an algebra with respect to convolution? A well-known sufficient condition is that $(w^{-q}*w^{-q})/w^{-q}$ be bounded on $\mathbb{Z}$, where $q:=p/(p-1)$ is the index conjugate to $p$. We present an example to show that this sufficient condition is not necessary.

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BibTeXRIS

Frédéric Morneau-Guérin, Thomas Ransford. 2026-11-02. A counterexample concerning weighted convolution on the integers. https://arxiv.org/abs/2611.03334

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