Laplace-Beltrami differentiability of positive definite kernels on the sphere

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• 作者：M. H. Castro (1)
  V. A. Menegatto (2)
  C. P. Oliveira (3)
  
• 关键词：Sphere ; Laplace ; Beltrami operator ; Laplace ; Beltrami derivative ; positive definite kernels ; spherical harmonics ; 33C55 ; 42A82 ; 43A85 ; 43A90 ; 44A35 ; 46G05
• 刊名：Acta Mathematica Sinica
• 出版年：2013
• 出版时间：January 2013
• 年：2013
• 卷：29
• 期：1
• 页码：93-104
• 全文大小：235KB
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• 作者单位：M. H. Castro (1)
  V. A. Menegatto (2)
  C. P. Oliveira (3)
  
  1. Faculdade de Matem谩tica, Universidade Federal de Uberl芒ndia, Caixa Postal 593 38400-902, Uberl芒ndia MG, Brasil
  2. Departamento de Matem谩tica, ICMC-USP, S茫o Carlos, Caixa Postal 668 13560-970, S茫o Carlos SP, Brasil
  3. ICE-DMC, Universidade Federal de Itajub谩, 37500-903, Itajub谩 MG, Brasil
  
• ISSN：1439-7617

文摘

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.