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    Closed form representations and properties of the generalised Wendland functions

    Chernih, A. and Hubbert, Simon (2016) Closed form representations and properties of the generalised Wendland functions. Working Paper. Birkbeck, University of London, London, UK.

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    Abstract

    In this paper we investigate the generalisation of Wendland’s compactly supported radial basis functions to the case where the smoothness parameter is not assumed to be a positive integer or half-integer and the parameter ℓ, which is chosen to ensure positive definiteness, need not take on the minimal value. We derive sufficient and necessary conditions for the generalised Wendland functions to be positive definite and deduce the native spaces that they generate. We also provide closed form representations for the generalised Wendland functions in the case when the smoothness parameter is an integer and where the parameter ℓ is any suitable value that ensures positive definiteness, as well as closed form representations for the Fourier transform when the smoothness parameter is a positive integer or half-integer.

    Metadata

    Item Type: Monograph (Working Paper)
    Additional Information: Birkbeck Pure Mathematics Preprint Series #22
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Research Centre: Applied Macroeconomics, Birkbeck Centre for
    Depositing User: Administrator
    Date Deposited: 22 Mar 2019 13:17
    Last Modified: 27 Jul 2019 21:19
    URI: http://eprints.bbk.ac.uk/id/eprint/26748

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