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

2014/01/13 by Jeff Ledford, Ledford, Jeff
Mathematics · #Approximation Theory and Sequence Spaces #Mathematical Analysis and Transform Methods #Mathematical Approximation and Integration #math.FA #msc:41A05 #msc:41A63

paper · pdf · doi:10.48550/arxiv.1401.2893

12 pages

arxiv created 2014/01/13 · arxiv updated 2014/01/14

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_Bβ, and shows that one may recover these functions from their samples on a complete interpolating sequence for [-δ,δ]² by using the Poisson interpolation operator, provided that 0<β< (3-√(8))δ.

Related

• Approximating Continuous Functions with Scattered Translates of the Poisson Kernel
• Irregular Sampling of the Radon Transform of Bandlimited Functions
• Multivariate polynomial interpolation and sampling in Paley-Wiener spaces
• Approximation of a Multivariate Function of Bounded Variation from its\n Scattered Data
• Dynamical sampling, derivatives, and interpolation formulas in the Paley--Wiener space