论文标题
免费谐波分析中的扩展问题
The extension problem in free harmonic analysis
论文作者
论文摘要
本文研究了谐波分析的某些方面对非亚伯自由群体的研究。我们专注于在自由组上具有正定功能的概念，我们的主要目标是了解如何将这些功能从有限半径的球扩展到整个组。先前的工作表明，这种扩展始终存在，我们研究了多个积极确定功能的同时扩展的问题。更具体地说，我们定义了一个“相对能量”的概念，该概念可以测量一对积极的确定函数之间的接近性，并表明在有限球上的一对阳性确定功能可以扩展到整个组而不增加其相对能量。该证明是分析性的，涉及非共同szego参数的分化。
This paper studies certain aspects of harmonic analysis on nonabelian free groups. We focus on the concept of a positive definite function on the free group and our primary goal is to understand how such functions can be extended from balls of finite radius to the entire group. Previous work showed that such extensions always exist and we study the problem of simultaneous extension of multiple positive definite functions. More specifically, we define a concept of 'relative energy' which measures the proximity between a pair of positive definite functions, and show that a pair of positive definite functions on a finite ball can be extended to the entire group without increasing their relative energy. The proof is analytic, involving differentiation of noncommutative Szego parameters.
