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Super-exponential decay rates for eigenvalues and singular values of integral operators on the sphere
This paper brings results about the behavior of sequences of eigenvalues or
singular values of integral operators generated by square-integrable kernels on
the real m-dimensional unit sphere, . Under smoothness assumptions on
the generating kernels, given via Laplace-Beltrami differentiability, we obtain
super-exponential decay rates for the eigenvalues of the generated positive
integral operators and for singular values of those integral operators which
are non-positive. We show an optimal-type result and provide a list of
parametric families of kernels which are of interest for numerical analysis and
geostatistical communities and satisfy the smoothness assumptions for the
positive case.Comment: 15 page