Strict positive definiteness of convolutional and axially symmetric kernels on d-dimensional spheres
Numerical Analysis
2021-05-07 v1 Numerical Analysis
Abstract
The paper introduces new sufficient conditions of strict positive definiteness for kernels on d-dimensional spheres which are not radially symmetric but possess specific coefficient structures. The results use the series expansion of the kernel in spherical harmonics. The kernels either have a convolutional form or are axially symmetric with respect to one axis. The given results on convolutional kernels generalise the result derived by Chen et al. [8] for radial kernels. Keywords: strictly positive definite kernels, covariance functions, sphere
Keywords
Cite
@article{arxiv.2105.02586,
title = {Strict positive definiteness of convolutional and axially symmetric kernels on d-dimensional spheres},
author = {Martin Buhmann and Janin Jäger},
journal= {arXiv preprint arXiv:2105.02586},
year = {2021}
}
Comments
arXiv admin note: text overlap with arXiv:2005.02798