论文标题
在维纳（Wiener）的引理中
On Wiener's lemma for locally compact abelian groups
论文作者
论文摘要
Inspired by an extension of Wiener's lemma on the relation of measures $μ$ on the unit circle and their Fourier coefficients $\widehatμ(k_n)$ along subsequences $(k_n)$ of the natural numbers by Cuny, Eisner and Farkas [CEF19, arXiv:1701.00101], we study the validity of the lemma when the Fourier coefficients are weighted by一系列概率度量。通过使用从这些度量序列得出的过滤器中使用收敛性，我们获得了相似的结果，现在还允许考虑本地紧凑的Abelian组以外的$ \ Mathbb {T} $和$ \ Mathbb {R} $。作为应用程序，我们提出了Goldstein [Gol96]对Semigroup对希尔伯特空间的作用的结果的扩展。
Inspired by an extension of Wiener's lemma on the relation of measures $μ$ on the unit circle and their Fourier coefficients $\widehatμ(k_n)$ along subsequences $(k_n)$ of the natural numbers by Cuny, Eisner and Farkas [CEF19, arXiv:1701.00101], we study the validity of the lemma when the Fourier coefficients are weighted by a sequence of probability measures. By using convergence with respect to a filter derived from these measure sequences, we obtain similar results, now also allowing the consideration of locally compact abelian groups other than $\mathbb{T}$ and $\mathbb{R}$. As an application, we present an extension of a result of Goldstein [Gol96] on the action of semigroups on Hilbert spaces.
