Characterization of positive definite, radial functions on free groups
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Published:2023-04-24
Issue:15
Volume:10
Page:168-181
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ISSN:2330-1511
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Container-title:Proceedings of the American Mathematical Society, Series B
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language:en
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Short-container-title:Proc. Amer. Math. Soc. Ser. B
Author:
Chuah Chian Yeong,Liu Zhenchuan,Mei Tao
Abstract
This article studies the properties of positive definite, radial functions on free groups following the work of Haagerup and Knudby [Proc. Amer. Math. Soc. 143 (2015), pp. 1477–1489]. We obtain characterizations of radial functions with respect to the
ℓ
2
\ell ^{2}
length on the free groups with infinite generators and the characterization of the positive definite, radial functions with respect to the
ℓ
p
\ell ^{p}
length on the free real line with infinite generators for
0
>
p
≤
2
0 > p \leq 2
. We obtain a Lévy-Khintchine formula for length-radial conditionally negative functions as well.
Funder
National Science Foundation
Publisher
American Mathematical Society (AMS)
Subject
Geometry and Topology,Discrete Mathematics and Combinatorics,Analysis,Algebra and Number Theory
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