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arXiv · 1401.2893

Recovery of bivariate band limited functions using scattered translates of the Poisson kernel

Jeff Ledford
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Abstract

This paper continues the study of interpolation operators on scattered data. We introduce the Poisson interpolation operator and prove various properties. The main result concerns functions in the Paley-Wiener space $PW_{B_\beta}$, and shows that one may recover these functions from their samples on a complete interpolating sequence for $[-\delta,\delta]^2$ by using the Poisson interpolation operator, provided that $0<\beta < (3-\sqrt{8})\delta$.

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Jeff Ledford. 2014-01-13. Recovery of bivariate band limited functions using scattered translates of the Poisson kernel. https://arxiv.org/abs/1401.2893

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