Geodesic
Uniqueness theorems for solutions of the convolution equation
Izvestiya. Mathematics , Tome 70 (2006) no. 6, pp. 1077-1092.

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Precise uniqueness theorems are proved for the solutions of a convolution equation on Riemannian symmetric spaces of non-compact type of rank $1$ and an application is given to lacunary series with respect to special functions. 
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V. V. Volchkov. Uniqueness theorems for solutions of the convolution equation. Izvestiya. Mathematics , Tome 70 (2006) no. 6, pp. 1077-1092. http://geodesic.mathdoc.fr/item/IM2_2006_70_6_a0/

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