Generalised Wendland functions for the sphere
Loading...
Date
Authors
Advisors/Reviewers
Further Contributors
Contributing Institutions
Publisher
Journal Title
Journal ISSN
Volume Title
Publisher
License
Quotable link
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 3F2 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.Link to publications or other datasets
Description
Notes
Original publication in
Advances in computational mathematics 49 (2023), 3