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dc.contributor.authorHubbert, Simon
dc.contributor.authorJäger, Janin
dc.date.accessioned2024-02-06T14:38:21Z
dc.date.available2024-02-06T14:38:21Z
dc.date.issued2023
dc.identifier.urihttps://jlupub.ub.uni-giessen.de//handle/jlupub/18952
dc.identifier.urihttp://dx.doi.org/10.22029/jlupub-18313
dc.description.abstractIn 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.
dc.description.sponsorshipDeutsche Forschungsgemeinschaft (DFG); ROR-ID:018mejw64
dc.language.isoen
dc.rightsNamensnennung 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subject.ddcddc:510
dc.subject.ddcddc:004
dc.titleGeneralised Wendland functions for the sphere
dc.typearticle
local.affiliationFB 07 - Mathematik und Informatik, Physik, Geographie
local.projectProjektnummer: 461449252
local.source.journaltitleAdvances in computational mathematics
local.source.volume49
local.source.articlenumber3
local.source.urihttps://doi.org/10.1007/s10444-022-10005-z


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