Laplace-Beltrami Differentiability of Positive Definite Kernels on the Sphere

被引：0

作者：

M. H. CASTRO ^{[1
]}

V. A. MENEGATTO ^{[2
]}

C. P. OLIVEIRA ^{[3
]}

机构：

[1] Faculdade de Matemática, Universidade Federal de Uberladia,Caixa Postal 593 38400-902, Uberlandia MG, Brasil

[2] Departamento de Matemática, ICMC-USP,Sao Carlos,Caixa Postal 668 13560-970, Sao Carlos SP, Brasil

[3] ICE-DMC, Universidade Federal de Itajubá,37500-903 Itajubá MG, Brasil

来源：

Acta Mathematica Sinica,English Series | 2013年 / 01期

基金：

巴西圣保罗研究基金会;

关键词：

Sphere; Laplace-Beltrami operator; Laplace-Beltrami derivative; positive definite kernels; spherical harmonics;

D O I：

暂无

中图分类号：

O174 [函数论];

学科分类号：

070104 ;

摘要：

This contribution gives results on the action of the Laplace-Beltrami derivative on sufficiently smooth kernels on the sphere, those defined by absolutely and uniformly expansions generated by a family of at least continuous functions. Among other things, the results show that convenient Laplace-Beltrami derivatives of positive definite kernels on the sphere are positive definite too. We also include similar results on the action of the Laplace-Beltrami derivative on condensed spherical harmonic expansions.

引用

页码：93 / 104

页数：12

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