Strictly positive definite functions on compact abelian groups

Details Strictly positive definite functions on compact abelian groups Strictly positive definite functions on compact abelian groups

2010-02-16

arxiv.org/abs/1002.3017v1

Mathematics

Functional Analysis

9 pages; submitted to Proc. AMS

Scientific paper

We study the Fourier characterisation of strictly positive definite functions
on compact abelian groups. Our main result settles the case $G = F \times
\mathbb{T}^r$, with $r \in \mathbb{N}$ and $F$ finite. The characterisation
obtained for these groups does not extend to arbitrary compact abelian groups;
it fails in particular for all torsion-free groups.

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