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. 
@article{MT_2011_14_2_a1,
     author = {V. L. Vaskevich},
     title = {Extremal functions of cubature formulas on a~multidimensional sphere and spherical splines},
     journal = {Matemati\v{c}eskie trudy},
     pages = {14--27},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2011_14_2_a1/}
}
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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/