Convolution equations and the local Pompeiu property on symmetric spaces and on phase space associated to the Heisenberg group

Abstract

In this paper, we present new uniqueness results related to geometric aspects of mean periodicity on various homogeneous spaces. Among these results, we point out the equivalence of the local and the global Pompeiu property for arbitrary families of compactly supported distributions, the solution of the local Pompeiu problem for the class of non real-analytic functions, and local versions of the two-radii theorem on symmetric spaces of arbitrary rank.