两点齐次流形上的严格正定非各向同性核:渐近方法

IF 0.8 3区数学 Q2 MATHEMATICS Positivity Pub Date : 2023-11-26 DOI:10.1007/s11117-023-01022-3

J. C. Guella, J. Jäger

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引用次数: 1

摘要

基于Laplace-Beltrami算子在本征函数中的展开式，给出了紧两点齐次空间上一类正定核族是严格正定的充分条件。我们也给出了这个内核类的一个特征。所分析的族是各向同性核的推广，并对实球的情况进行了详细的分析。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Strictly positive definite non-isotropic kernels on two-point homogeneous manifolds: the asymptotic approach

We present sufficient conditions for a family of positive definite kernels on a compact two-point homogeneous space to be strictly positive definite based on their expansion in eigenfunctions of the Laplace–Beltrami operator. We also present a characterisation of this kernel class. The family analyzed is a generalization of the isotropic kernels and the case of a real sphere is analyzed in details.

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来源期刊

Positivity 数学-数学

CiteScore

1.80

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： The purpose of Positivity is to provide an outlet for high quality original research in all areas of analysis and its applications to other disciplines having a clear and substantive link to the general theme of positivity. Specifically, articles that illustrate applications of positivity to other disciplines - including but not limited to - economics, engineering, life sciences, physics and statistical decision theory are welcome. The scope of Positivity is to publish original papers in all areas of mathematics and its applications that are influenced by positivity concepts.