论文标题
Brascamp-Lieb不平等中的傅立叶二元性
Fourier duality in the Brascamp-Lieb inequality
论文作者
论文摘要
最近在Bez，Buschenhenke，Cowling，Flock和第一作者的工作中观察到，Euclidean Brascamp-Lieb不平等能够满足自然而有用的傅立表双重性能。本文的目的是建立适当的离散类似物。我们的主要结果是在其（Pontryagin）双重的（Pontryagin）双重的（有限生成的）离散的Abelian团体上确定了（有限生成的）离散的Abelian群体。正如显而易见的那样，这种二元性原理的自然环境是本地紧凑的阿贝尔群体的自然环境，这提出了有关这种一般性中制定的Brascamp-lieb常数的基本问题。
It was observed recently in work of Bez, Buschenhenke, Cowling, Flock and the first author, that the euclidean Brascamp-Lieb inequality satisfies a natural and useful Fourier duality property. The purpose of this paper is to establish an appropriate discrete analogue of this. Our main result identifies the Brascamp-Lieb constants on (finitely-generated) discrete abelian groups with Brascamp-Lieb constants on their (Pontryagin) duals. As will become apparent, the natural setting for this duality principle is that of locally compact abelian groups, and this raises basic questions about Brascamp-Lieb constants formulated in this generality.
