BIROn - Birkbeck Institutional Research Online

    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.

    [img] Text
    WendSphereDONE.pdf - Author's Accepted Manuscript
    Restricted to Repository staff only

    Download (356kB)
    [img]
    Preview
    Text
    49521a.pdf - Published Version of Record
    Available under License Creative Commons Attribution.

    Download (1MB) | Preview

    Abstract

    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.

    Metadata

    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: 02 Aug 2023 18:18
    URI: https://eprints.bbk.ac.uk/id/eprint/49521

    Statistics

    Activity Overview
    6 month trend
    27Downloads
    6 month trend
    119Hits

    Additional statistics are available via IRStats2.

    Archive Staff Only (login required)

    Edit/View Item Edit/View Item