Journal article

Publication year: 2022

Pages: 1500-1525

Journal: IMA Journal of Numerical Analysis

Volume number: 42

Issue number: 2

ISSN: 0272-4979

eISSN: 1464-3642

Open access status: Green

DOI Link: https://doi.org/10.1093/imanum/drab012

Publisher: Oxford University Press

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.

Harvard Citation style: Buhmann, M. and Jaeger, J. (2022) Strictly positive definite kernels on the 2-sphere: from radial symmetry to eigenvalue block structure, IMA Journal of Numerical Analysis, 42(2), pp. 1500-1525. https://doi.org/10.1093/imanum/drab012

APA Citation style: Buhmann, M., & Jaeger, J. (2022). Strictly positive definite kernels on the 2-sphere: from radial symmetry to eigenvalue block structure. IMA Journal of Numerical Analysis. 42(2), 1500-1525. https://doi.org/10.1093/imanum/drab012