Affiliation:
1. Lehrstuhl Numerische Mathematik, Justus-Liebig University, Heinrich-Buff Ring 44, 35392 Giessen, Germany
Abstract
Abstract
The paper introduces a new characterization of strict positive definiteness for kernels on the 2-sphere without assuming the kernel to be radially (isotropic) or axially symmetric. The results use the series expansion of the kernel in spherical harmonics. Then additional sufficient conditions are proven for kernels with a block structure of expansion coefficients. These generalize the result derived by Chen et al. (2003, A necessary and sufficient condition for strictly positive definite functions on spheres. Proc. Amer. Math. Soc., 131, 2733–2740) for radial kernels to nonradial kernels.
Publisher
Oxford University Press (OUP)
Subject
Applied Mathematics,Computational Mathematics,General Mathematics
Cited by
1 articles.
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