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

Authors :
Castro, M. H.
Jordão, T.
Peron, A. P.
Publication Year :
2017

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.<br />Comment: 15 pages

Subjects

Subjects :
Mathematics - Functional Analysis

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.1708.02575
Document Type :
Working Paper
Full Text :
https://doi.org/10.1016/j.cam.2019.06.050