On the Convergence of Regular Families of Cardinal Interpolators

TL;DR

This paper introduces a general framework for constructing cardinal interpolants for l^2-data on integer lattices, including a parameter to recover the original Paley-Wiener function, enhancing interpolation methods.

Contribution

It presents a novel general approach to develop cardinal interpolants for l^2-data and introduces a parameter for recovering the original Paley-Wiener function.

Findings

Provides a unified method for cardinal interpolation on Z^n

Introduces a parameter enabling recovery of the original Paley-Wiener function

Enhances understanding of convergence properties of interpolants

Abstract

In this note a general way to develop a cardinal interpolant for $l^2$-data on the integer lattice $Z^n$ is shown. Further, a parameter is introduced which allows one to recover the original Paley-Weiner function from which the data came.