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On the Gibbs–Wilbraham Phenomenon for Sampling and Interpolatory Series

Part of: Approximations and expansions Nontrigonometric harmonic analysis

Published online by Cambridge University Press:  12 July 2019

Keaton Hamm
Keaton Hamm*
Affiliation:
Department of Mathematics, University of Arizona, Tucson, AZ, 85721, USA (hamm@math.arizona.edu)
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Abstract

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

Keywords

Gibbs phenomenongeneralized sampling kernelscardinal functionssampling expansions

MSC classification

Primary: 41A05: Interpolation
Secondary: 41A30: Approximation by other special function classes 42C15: General harmonic expansions, frames
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 4 , November 2019 , pp. 1163 - 1171
Copyright
Copyright © Edinburgh Mathematical Society 2019 

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Footnotes

To N. Sivakumar

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