Journal article

Publication year: 2023

Journal: Advances in Computational Mathematics

Volume number: 49

Issue number: 1

ISSN: 1019-7168

eISSN: 1572-9044

Open access status: Hybrid

DOI Link: https://doi.org/10.1007/s10444-022-10005-z

Publisher: Springer

Abstract: 
In this paper, we compute the spherical Fourier expansion coefficients for the restriction of the generalised Wendland functions from d-dimensional Euclidean space to the (d - 1)-dimensional unit sphere. We use results from the theory of special functions to show that they can be expressed in a closed form as a multiple of a certain F-3(2) hypergeometric function. We present tight asymptotic bounds on the decay rate of the spherical Fourier coefficients and, in the case where d is odd, we are able to provide the precise asymptotic rate of decay. Numerical evidence suggests that this precise asymptotic rate also holds when d is even and we pose this as an open problem. Finally, we observe a close connection between the asymptotic decay rate of the spherical Fourier coefficients and that of the corresponding Euclidean Fourier transform.

Harvard Citation style: Hubbert, S. and Jaeger, J. (2023) Generalised Wendland functions for the sphere, Advances in Computational Mathematics, 49(1), Article 3. https://doi.org/10.1007/s10444-022-10005-z

APA Citation style: Hubbert, S., & Jaeger, J. (2023). Generalised Wendland functions for the sphere. Advances in Computational Mathematics. 49(1), Article 3. https://doi.org/10.1007/s10444-022-10005-z