Strictly positive definite functions on compact abelian groups

2010/02/16 by Jan Emonds, Emonds, Jan, Hartmut Fuehr +1
Mathematics · #43A25 #43A75 #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #math.FA #math.GR #msc:43A25 #msc:43A75

paper · pdf · doi:10.48550/arxiv.1002.3017

9 pages; submitted to Proc. AMS

arxiv created 2010/02/16 · arxiv updated 2010/02/26

Abstract

We study the Fourier characterisation of strictly positive definite functions on compact abelian groups. Our main result settles the case G = F × \mathbbT^r, with r ∈ 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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