Abstract
On a two-point homogeneous space X, we consider the problem of describing the set of continuous functions having zero integrals over all spheres enclosing the given ball. We obtain the solution of this problem and its generalizations for an annular domain in X. By way of applications, we prove new uniqueness theorems for functions with zero spherical means.
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Original Russian Text © V. V. Volchkov, Vit. V. Volchkov, 2017, published in Matematicheskie Zametki, 2017, Vol. 101, No. 3, pp. 359–372.
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Volchkov, V.V., Volchkov, V.V. Analogs of the Globevnik problem on Riemannian two-point homogeneous spaces. Math Notes 101, 417–428 (2017). https://doi.org/10.1134/S000143461703004X
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DOI: https://doi.org/10.1134/S000143461703004X