2020
DOI: 10.1016/j.cam.2019.06.050
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Super-exponential decay rates for eigenvalues and singular values of integral operators on the sphere

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 ≥ 2. Under smoothness assumptions on the kernels, given via (infinitely many times) Laplace-Beltrami differentiability, we obtain super-exponential decay rates for the eigenvalues of positive integral operators and for singular values of those which are non-positive. The positive case is shown to be optimal. We also pro… Show more

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