Laplace-Beltrami Differentiability of Positive Definite Kernels on the Sphere  

作　　者：M. H. CASTRO V. A. MENEGATTO C. P. OLIVEIRA 

机构地区：[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

出　　处：《Acta Mathematica Sinica,English Series》2013年第1期93-104,共12页数学学报（英文版）

基　　金：supported by CAPES-Brasil;supported by FAPESP-Brasil(Grant No.2010/19734-6)

摘　　要：This contribution gives results on the action of the Laplace-Beltrami derivative on suffi- ciently 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.This contribution gives results on the action of the Laplace-Beltrami derivative on suffi- ciently 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.

关 键 词：SPHERE Laplace-Beltrami operator Laplace-Beltrami derivative positive definite kernels spherical harmonics 

分 类 号：O174[理学—数学]