Geodesic
Harmonic functions representable by integrals of Green type.~I
Izvestiya. Mathematics , Tome 1 (1967) no. 1, pp. 139-149.

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We introduce the concepts of an integral of Green–Lebesgue type and the integral of Green–Lebesgue which generalizes the classical representation of a harmonic function inside a closed surface $S$ by means of Green's formula. We give conditions for representability of a harmonic function by integrals of the above types. In this part of the work we consider the case of the unit sphere $S$. 
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E. D. Solomentsev. Harmonic functions representable by integrals of Green type.~I. Izvestiya. Mathematics , Tome 1 (1967) no. 1, pp. 139-149. http://geodesic.mathdoc.fr/item/IM2_1967_1_1_a8/

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