# Structure of the Set of Signals With Strong Divergence of the Shannon Sampling Series

Abstract:

It is known that there exist signals in Paley-Wiener space $PW_\pi^1$ 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 $PW_\pi^1$, all signals of which, except the zero signal, lead to strong divergence of the peak value of the Shannon sampling series.

## icassp2017_structure_poster.pdf

### Paper Details

Authors:
Holger Boche, Ullrich J. Mönich, Ezra Tampubolon
Submitted On:
2 March 2017 - 5:48am
Type:
Poster
Event:
Document Year:
2017

(280)

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[1] Holger Boche, Ullrich J. Mönich, Ezra Tampubolon, "Structure of the Set of Signals With Strong Divergence of the Shannon Sampling Series", IEEE SigPort, 2017. [Online]. Available: http://sigport.org/1579. Accessed: Jun. 25, 2019.
@article{1579-17,
url = {http://sigport.org/1579},
author = {Holger Boche; Ullrich J. Mönich; Ezra Tampubolon },
publisher = {IEEE SigPort},
title = {Structure of the Set of Signals With Strong Divergence of the Shannon Sampling Series},
year = {2017} }
TY - EJOUR
T1 - Structure of the Set of Signals With Strong Divergence of the Shannon Sampling Series
AU - Holger Boche; Ullrich J. Mönich; Ezra Tampubolon
PY - 2017
PB - IEEE SigPort
UR - http://sigport.org/1579
ER -
Holger Boche, Ullrich J. Mönich, Ezra Tampubolon. (2017). Structure of the Set of Signals With Strong Divergence of the Shannon Sampling Series. IEEE SigPort. http://sigport.org/1579
Holger Boche, Ullrich J. Mönich, Ezra Tampubolon, 2017. Structure of the Set of Signals With Strong Divergence of the Shannon Sampling Series. Available at: http://sigport.org/1579.
Holger Boche, Ullrich J. Mönich, Ezra Tampubolon. (2017). "Structure of the Set of Signals With Strong Divergence of the Shannon Sampling Series." Web.
1. Holger Boche, Ullrich J. Mönich, Ezra Tampubolon. Structure of the Set of Signals With Strong Divergence of the Shannon Sampling Series [Internet]. IEEE SigPort; 2017. Available from : http://sigport.org/1579