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arXiv · 1708.02575

Super-exponential decay rates for eigenvalues and singular values of integral operators on the sphere

M. H. Castro·T. Jordão·A. P. Peron
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Abstract

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, $m\leq2$. 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.

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M. H. Castro, T. Jordão, A. P. Peron. 2017-08-08. Super-exponential decay rates for eigenvalues and singular values of integral operators on the sphere. https://doi.org/10.1016/j.cam.2019.06.050

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