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On the convergence of regular families of cardinal interpolators

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Abstract

In this article, we develop a one parameter family of cardinal interpolants associated to a function ϕ. The main theorem gives conditions on ϕ and the parameter that allow Paley-Wiener functions to be recovered from their samples on the integer lattice \(\mathbb {Z}^{n}\). Our methods unify previous work done on splines and the Gaussian and provide new examples of this phenomenon, including two families of multiquadrics.

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Authors and Affiliations

  1. University of Connecticut, Storrs, CT, 06269, USA

    Jeff Ledford

  2. Virginia Commonwealth University, Richmond, VA, 23284, USA

    Jeff Ledford

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  1. Jeff Ledford
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Correspondence to Jeff Ledford.

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Communicated by: T. Lyche

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Ledford, J. On the convergence of regular families of cardinal interpolators. Adv Comput Math 41, 357–371 (2015). https://doi.org/10.1007/s10444-014-9361-4

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  • DOI: https://doi.org/10.1007/s10444-014-9361-4

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