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

2019/03/15 by Keaton Hamm, Hamm, Keaton
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA

paper · pdf · doi:10.48550/arxiv.1903.06698

To appear in Proceedings of the Edinburgh Mathematical Society

arxiv created 2019/03/15 · arxiv updated 2019/03/18

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.

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