Geodesic
Uniqueness theorems for some classes of functions with zero spherical means
Matematičeskie zametki, Tome 62 (1997) no. 1, pp. 59-65

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We study various classes of functions that have zero integrals over all spheres of given radius. For these functions, we obtain a description in the form of a series in special functions; the problem of the existence of a nonzero function of prescribed growth with this property is completely solved. 
@article{MZM_1997_62_1_a5,
     author = {V. V. Volchkov},
     title = {Uniqueness theorems for some classes of functions with zero spherical means},
     journal = {Matemati\v{c}eskie zametki},
     pages = {59--65},
     publisher = {mathdoc},
     volume = {62},
     number = {1},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_62_1_a5/}
}
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V. V. Volchkov. Uniqueness theorems for some classes of functions with zero spherical means. Matematičeskie zametki, Tome 62 (1997) no. 1, pp. 59-65. http://geodesic.mathdoc.fr/item/MZM_1997_62_1_a5/