Geodesic
Analogs of the Globevnik Problem on Riemannian Two-Point Homogeneous Spaces
Matematičeskie zametki, Tome 101 (2017) no. 3, pp. 359-372

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: spherical means, two-point homogeneous space, transmutation operator. 
@article{MZM_2017_101_3_a3,
     author = {V. V. Volchkov and Vit. V. Volchkov},
     title = {Analogs of the {Globevnik} {Problem} on {Riemannian} {Two-Point} {Homogeneous} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {359--372},
     publisher = {mathdoc},
     volume = {101},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_3_a3/}
}
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V. V. Volchkov; Vit. V. Volchkov. Analogs of the Globevnik Problem on Riemannian Two-Point Homogeneous Spaces. Matematičeskie zametki, Tome 101 (2017) no. 3, pp. 359-372. http://geodesic.mathdoc.fr/item/MZM_2017_101_3_a3/