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arXiv · 2112.00630

Characterization of positive definite, radial functions on free groups

Chian Yeong Chuah·Zhen-Chuan Liu·Tao Mei
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Abstract

This article studies the properties of positive definite, radial functions on free groups following the work of Haagerup and Knudby . We obtain characterizations of radial functions with respect to the $\ell^{2}$ length on the free groups with infinite generators and the characterization of the positive definite, radial functions with respect to the $\ell^{p}$ length on the free real line with infinite generators for $0 < p \leq 2$. We obtain the Levi-Khintchine formulas for length-radial conditionally negative functions as well.

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Chian Yeong Chuah, Zhen-Chuan Liu, Tao Mei. 2021-12-01. Characterization of positive definite, radial functions on free groups. https://arxiv.org/abs/2112.00630

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