# On the Gibbs--Wilbraham Phenomenon for Sampling and Interpolatory Series

## TL;DR

This paper investigates the Gibbs--Wilbraham phenomenon in generalized sampling and interpolation series, proving the existence of overshoot characteristics for certain cardinal functions and sampling series.

## Contribution

It provides new theoretical insights into the conditions under which overshoot occurs in sampling and interpolatory series, expanding understanding of the phenomenon.

## Key findings

- Existence of overshoot characteristic for certain cardinal functions
- Characterization of overshoot existence in sampling series
- Theoretical framework for Gibbs--Wilbraham phenomenon in sampling contexts

## Abstract

The Gibbs--Wilbraham phenomenon for generalized sampling series, and related interpolation series arising from cardinal functions is investigated. We prove existence of the overshoot characteristic of the phenomenon for certain cardinal functions, and characterize existence of an overshoot for sampling series.