球面上积分算子特征值和奇异值的超指数衰减率
Super-exponential decay rates for eigenvalues and singular values of integral operators on the sphere
摘要：
本文给出了m维实单位球面$m\leq2$上由平方可积核生成的积分算子的特征值或奇异值序列的性质.在生成核的光滑性假设下，通过Laplace-Beltrami可微性，我们得到了生成的正积分算子的特征值和非正的积分算子的奇异值的超指数衰减率.我们展示了一个最佳类型的结果，并提供了一个列表的参数家庭的内核感兴趣的数值分析和地质统计学社区，并满足平滑假设的积极的情况下。
英文摘要：
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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