Abstract:
Consider those functions on the $n$-dimensional sphere that have zero
integrals over all geodesic balls with centres in a given set $E$.
We obtain a description of such functions in the case when $E$ is a geodesic
sphere on $\mathbb S^n$. We also find a criterion for the existence
of non-zero functions with this property in the case when the set of centres
is the union of two geodesic spheres. We obtain analogues of these results
for quasi-analytic classes of functions.
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