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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.24578 |
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Table of Contents:
- Suppose that $G$ is a compact Hausdorff Abelian group. We say $μ\in M(G)$ is strongly continuous if $|μ|(x+H)=0$ for any $x \in G$ and any $H \leq G$ that is closed and of infinite index. We prove that for any sufficiently rapidly decreasing sequence $(a_{n})_{n=1}^{\infty}\in c_{0}(\mathbb{N})$, for every strongly continuous $μ\in M(G)$ with $\|μ\| \leq 1$ and $\widehatμ(\widehat{G})\subset \{a_n: n \in \mathbb{N}\}\cup\{0\}$, the measure $μ\astμ$ is absolutely continuous with respect to Haar measure on $G$. This implies that $μ$ does not exhibit the so-called Wiener-Pitt phenomenon. The paper is a continuation of investigations started in \cite{ow}.