Heat properties for groups
Abstract
We revisit Fourier's approach to solve the heat equation on the circle in the context of (twisted) reduced group C*-algebras, convergence of Fourier series and semigroups associated to negative definite functions. We introduce some heat properties for countably infinite groups and investigate when they are satisfied. Kazhdan's property (T) is an obstruction to the weakest property, and our findings leave open the possibility that this might be the only one. On the other hand, many groups with the Haagerup property satisfy the strongest version. We show that this heat property implies that the associated heat problem has a unique solution regardless of the choice of the initial datum.
Keywords
Cite
@article{arxiv.2211.12321,
title = {Heat properties for groups},
author = {Erik Bédos and Roberto Conti},
journal= {arXiv preprint arXiv:2211.12321},
year = {2026}
}
Comments
Very minor changes. Few typos have been corrected and a reference has been added. To appear in J. Fourier Anal. Appl