具有平移有界测度的回火分布的傅里叶变换和广义Eberlein分解
Tempered distributions with translation bounded measure as Fourier transform and the generalized Eberlein decomposition
摘要：
本文研究了一类傅里叶变换为平移有界测度的调和分布，证明了$\mathbb{R}^d$中的每一个这样的分布至多有$2d$阶.我们证明了广义Eberlein分解在这类分布的存在性，以及它与所有以前的Eberlein分解的兼容性。讨论了Fourier可变换测度的广义Eberlein分解及其分支的性质。最后，我们仔细研究了Meyer集上支持的绝对连续谱。
英文摘要：
In this paper, we study the class of tempered distributions whose Fourier transform is a translation bounded measure and show that each such distribution in $\mathbb{R}^d$ has order at most $2d$. We show the existence of the generalized Eberlein decomposition within this class of distributions, and its compatibility with all previous Eberlein decompositions. The generalized Eberlein decomposition for Fourier transformable measures and properties of its components are discussed. Lastly, we take a closer look at the absolutely continuous spectrum of measures supported on Meyer sets.
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