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We generalize and extend results on decay rates of singular values oreigenvalues of positive integral operators from unit spheres to two-pointhomogeneous spaces. The rates we present depend upon the order of theLaplace-Beltrami operator used to define the smoothness conditions ongenerating kernels, the Schatten class containing the integral operatorgenerated by the derivative of the generating kernel and the dimension of thespace.

Eigenvalue decay of positive integral operators on compact two-point homogeneous spaces