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

Abstract

We generalize and extend results on decay rates of singular values or eigenvalues of positive integral operators from unit spheres to two-point homogeneous spaces. The rates we present depend upon the order of the Laplace-Beltrami operator used to define the smoothness conditions on generating kernels, the Schatten class containing the integral operator generated by the derivative of the generating kernel and the dimension of the space.