Geodesic
Uniqueness theorems for some classes of functions with zero spherical means
Matematičeskie zametki, Tome 62 (1997) no. 1, pp. 59-65 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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