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- Title
Characterization of positive definite, radial functions on free groups.
- Authors
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 \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 a Lévy-Khintchine formula for length-radial conditionally negative functions as well.
- Subjects
INFINITE groups; GENERATORS of groups; FREE groups
- Publication
Proceedings of the American Mathematical Society, Series B, 2023, Vol 10, p168
- ISSN
2330-1511
- Publication type
Article
- DOI
10.1090/bproc/158