Cubature Formulas, Geometrical Designs, Reproducing Kernels, and Markov Operators
Cubature Formulas, Geometrical Designs, Reproducing Kernels, and Markov Operators
Cubature formulas and geometrical designs are described in terms of reproducing kernels for Hilbert spaces of functions on the one hand, and Markov operators associated to orthogonal group representations on the other hand. In this way, several known results for spheres in Euclidean spaces, involving cubature formulas for polynomial functions …