Strict Positive Definiteness of Convolutional and Axially Symmetric Kernels on <i>d</i>-Dimensional Spheres - Research portal of Justus Liebig University Giessen:

Journal article

Strict Positive Definiteness of Convolutional and Axially Symmetric Kernels on d-Dimensional Spheres

Authors list: Buhmann, Martin; Jaeger, Janin

Publication year: 2022

Journal: Journal of Fourier Analysis and Applications

Volume number: 28

Issue number: 3

ISSN: 1069-5869

eISSN: 1531-5851

Open access status: Hybrid

DOI Link: https://doi.org/10.1007/s00041-022-09913-x

Publisher: Springer

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. (Proc Am Math Soc 131:2733-2740, 2003) for radial kernels.

Citation Styles

Harvard Citation style: Buhmann, M. and Jaeger, J. (2022) Strict Positive Definiteness of Convolutional and Axially Symmetric Kernels on d-Dimensional Spheres, Journal of Fourier Analysis and Applications, 28(3), Article 40. https://doi.org/10.1007/s00041-022-09913-x

APA Citation style: Buhmann, M., & Jaeger, J. (2022). Strict Positive Definiteness of Convolutional and Axially Symmetric Kernels on d-Dimensional Spheres. Journal of Fourier Analysis and Applications. 28(3), Article 40. https://doi.org/10.1007/s00041-022-09913-x

Keywords

Covariance functions; Sphere; Strictly positive definite kernels

SDG Areas

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