Differentiable positive definite functions on two-point homogeneous spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:434

Article

Barbosa, V. S.¹  Menegatto, V. A.¹ 

[1] ICMC USP Sao Carlos, Dept Matemat, BR-13560970 Sao Carlos, SP, Brazil

关键词: Positive definite kernels;    Isotropic kernels;    Homogeneous spaces;    Jacobi polynomials;    Differentiability;   

DOI  :  10.1016/j.jmaa.2015.09.040

来源: Elsevier

【 摘 要 】

In this paper we study continuous kernels on compact two point homogeneous spaces which are positive definite and zonal (isotropic). Such kernels were characterized by R. Gangolli some forty years ago and are very useful for solving scattered data interpolation problems on the spaces. In the case the space is the d-dimensional unit sphere, J. Ziegel showed in 2013 that the radial part of a continuous positive definite and zonal kernel is continuously differentiable up to order right perpendicular(d-1)/2left perpendicular in the interior of its domain. The main issue here is to obtain a similar result for all the other compact two point homogeneous spaces. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free