论文标题
以卷积为特征的整体变换
Integral transforms characterized by convolution
论文作者
论文摘要
受果酱对特定组对傅立叶变换的特征的启发，我们提供了一种新颖的方法，该方法表征了任何局部紧凑的阿贝尔群体上的傅立叶变换。特别是，我们的特征包括果酱的结果。此外，我们证明了余弦变换以及拉普拉斯变换也可以通过合适的卷积特性来表征。
Inspired by Jaming's characterization of the Fourier transform on specific groups via the convolution property, we provide a novel approach which characterizes the Fourier transform on any locally compact abelian group. In particular, our characterization encompasses Jaming's results. Furthermore, we demonstrate that the cosine transform as well as the Laplace transform can also be characterized via a suitable convolution property.
