Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773732 | Journal of Approximation Theory | 2017 | 18 Pages |
Abstract
In this paper the structure of the set of functions for which the peak value of the Shannon sampling series is strongly divergent is analyzed. Strong divergence is closely linked to the non-existence of adaptive reconstruction methods. Signals in the Paley-Wiener space PWÏ1 of bandlimited functions with absolutely integrable Fourier transform are considered, and it is shown that the set of strong divergence is spaceable and dense-lineable, i.e., that there exist an infinite dimensional closed subspace and an infinite dimensional dense subspace, such that we have strong divergence of the peak value of the Shannon sampling series for all functions from these sets, except the zero function. Further, it is proved that this result is not restricted to the Shannon sampling series, but rather holds for an entire class of reconstruction processes.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Holger Boche, Ullrich J. Mönich, Ezra Tampubolon,