Structure of the set of signals with strong divergence of the Shannon sampling series
Holger Boche, Ullrich J. Mönich, Ezra Tampubolon
Abstract
It is known that there exist signals in Paley-Wiener space PW <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">π</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> of bandlimited signals with absolutely integrable Fourier transform, for which the peak value of the Shannon sampling series diverges unboundedly. In this paper we analyze the structure of the set of signals which lead to strong divergence. Strong divergence is closely linked to the existence of adaptive methods. We prove that there exists an infinite dimensional closed subspace of PW1 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">π</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> , all signals of which, except the zero signal, lead to strong divergence of the peak value of the Shannon sampling series.
BibTeX
@inproceedings{icassp2017_structureofthese,
title = {Structure of the set of signals with strong divergence of the Shannon sampling series},
author = {Holger Boche and Ullrich J. Mönich and Ezra Tampubolon},
booktitle = {ICASSP 2017},
year = {2017}
}