Journalartikel

Jahr der Veröffentlichung: 2022

Zeitschrift: Journal of Fourier Analysis and Applications

Bandnummer: 28

Heftnummer: 3

ISSN: 1069-5869

eISSN: 1531-5851

Open Access Status: Hybrid

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

Verlag: 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.

Harvard-Zitierstil: 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-Zitierstil: 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