Geodesic
Extremal functions of cubature formulas on a~multidimensional sphere and spherical splines
Matematičeskie trudy, Tome 14 (2011) no. 2, pp. 14-27.

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We establish the general form of extremal cubature formulas on multidimensional spheres. The domains of definition for the cubature formulas under consideration are Sobolev-type spaces on the sphere. The smoothness of the class function under study may be fractional. We prove that, for a given set of nodes, there exists a one-to-one correspondence between the set of extremal functions of cubature formulas on the sphere and the set of natural spherical splines with zero spherical mean. 
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V. L. Vaskevich. Extremal functions of cubature formulas on a~multidimensional sphere and spherical splines. Matematičeskie trudy, Tome 14 (2011) no. 2, pp. 14-27. http://geodesic.mathdoc.fr/item/MT_2011_14_2_a1/

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