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arXiv · 1002.3017

Strictly positive definite functions on compact abelian groups

Jan Emonds·Hartmut Fuehr
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Abstract

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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Jan Emonds, Hartmut Fuehr. 2010-02-16. Strictly positive definite functions on compact abelian groups. https://arxiv.org/abs/1002.3017

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