The two-sided Pompeiu problem for discrete groups

Linnell, Peter; Puls, Michael

doi:10.1090/bproc/124

The two-sided Pompeiu problem for discrete groups
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by Peter A. Linnell and Michael J. Puls HTML | PDF

Proc. Amer. Math. Soc. Ser. B 9 (2022), 221-229

Abstract:

We consider a two-sided Pompeiu type problem for a discrete group $G$. We give necessary and sufficient conditions for a finite subset $K$ of $G$ to have the $\mathcal {F}(G)$-Pompeiu property. Using group von Neumann algebra techniques, we give necessary and sufficient conditions for $G$ to be an $\ell ^2(G)$-Pompeiu group.

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