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    Generalised Wendland functions for the sphere

    Hubbert, Simon and Janin, J. (2023) Generalised Wendland functions for the sphere. Advances in Computational Mathematics 49 (3), ISSN 1019-7168.

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    In this paper we compute the spherical Fourier expansions 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 $_{3}F_{2}$ 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.


    Item Type: Article
    School: Birkbeck Faculties and Schools > Faculty of Business and Law > Birkbeck Business School
    Depositing User: Simon Hubbert
    Date Deposited: 15 Dec 2022 06:50
    Last Modified: 14 Mar 2024 09:26


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