The Pompeiu Problem and Discrete Groups

Details The Pompeiu Problem and Discrete Groups The Pompeiu Problem and Discrete Groups

2012-02-11

arxiv.org/abs/1202.2398v1

Mathematics

Functional Analysis

Scientific paper

We formulate a version of the Pompeiu problem in the discrete group setting.
Necessary and sufficient conditions are given for a finite collection of finite
subsets of a discrete abelian group, whose torsion free rank is less than the
cardinal of the continuum, to have the Pompeiu property. We also prove a
similar result for nonabelian free groups.

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