论文标题
措施的（扭曲的）埃伯林卷积
The (twisted) Eberlein convolution of measures
论文作者
论文摘要
在本文中，我们研究了Eberlein卷积的措施卷积的特性，并引入了它的扭曲版本。对于功能，我们表明扭曲的埃伯林卷积可以看作是翻译不变功能值的内部产品。我们研究其规律性特性，并显示其在合适的功能集上的存在。对于翻译有限的度量，我们表明（扭曲的）Eberlein卷积始终存在于给定序列的子序列，并且是一种微弱的周期性和傅立叶可转换度量。我们证明，如果这两个度量中的一种几乎是周期性的，那么（扭曲的）埃伯林卷积几乎是周期性的。此外，如果其中一种措施几乎是周期性的，那么（扭曲的）Eberlein卷积也是如此。
In this paper, we study the properties of the Eberlein convolution of measures and introduce a twisted version of it. For functions we show that the twisted Eberlein convolution can be seen as a translation invariant function-valued inner product. We study its regularity properties and show its existence on suitable sets of functions. For translation bounded measures we show that the (twisted) Eberlein convolution always exists along subsequences of the given sequence, and is a weakly almost periodic and Fourier transformable measure. We prove that if one of the two measures is mean almost periodic, then the (twisted) Eberlein convolution is strongly almost periodic. Moreover, if one of the measures is norm almost periodic, so is the (twisted) Eberlein convolution.
