A generalization of the exponential sampling series and its approximation properties

TL;DR

This paper introduces a generalized exponential sampling series, proves its convergence properties, and compares its approximation error with classical methods for Mellin band-limited functions.

Contribution

It extends the exponential sampling series framework, providing new convergence theorems and error estimates for a broader class of functions.

Findings

Established pointwise and uniform convergence theorems.

Derived quantitative error bounds for approximation.

Compared approximation errors between classical and generalized series.

Abstract

Here we introduce a generalization of the exponential sampling series of optical physics and establish pointwise and uniform convergence theorem, also in a quantitative form. Moreover we compare the error of approximation for Mellin band-limited functions using both classical and generalized exponential sampling series.