Sinc approximation of algebraically decaying functions

TL;DR

This paper extends sinc interpolation techniques to algebraically decaying functions, providing new error estimates and numerical validation for this class of functions.

Contribution

It introduces two types of error estimates for sinc approximation of algebraically decaying functions, broadening the applicability of sinc interpolation.

Findings

Error estimates for algebraic decay functions established

Applicable to functions with decay estimable in complex plane strip

Numerical examples validate theoretical results

Abstract

An extension of sinc interpolation on $\mathbb{R}$ to the class of algebraically decaying functions is developed in the paper. Similarly to the classical sinc interpolation we establish two types of error estimates. First covers a wider class of functions with the algebraic order of decay on $\mathbb{R}$. The second type of error estimates governs the case when the order of function's decay can be estimated everywhere in the horizontal strip of complex plane around $\mathbb{R}$. The numerical examples are provided.