Please use this identifier to cite or link to this item: https://doi.org/10.1006/jmaa.2001.7479
Title: Stability of the shifts of global supported distributions
Authors: Sun, Q. 
Issue Date: 1-Sep-2001
Citation: Sun, Q. (2001-09-01). Stability of the shifts of global supported distributions. Journal of Mathematical Analysis and Applications 261 (1) : 113-125. ScholarBank@NUS Repository. https://doi.org/10.1006/jmaa.2001.7479
Abstract: For a tempered distribution with ℓ1 decay, we characterize its stable shifts via its Fourier transform and via a shift-invariant space of summable sequences. Also we show that if the tempered distribution with ℓ1 decay has stable shifts, then we can recover all distributions in V∞, the space of all linear combinations of its shifts using bounded sequences, in a stable way using C∞ dual functions with ℓ1 decay at infinity. If, additionally, that tempered distribution is compactly supported, then the above C∞ dual functions can be chosen to have exponential decay at infinity. © 2001 Academic Press.
Source Title: Journal of Mathematical Analysis and Applications
URI: http://scholarbank.nus.edu.sg/handle/10635/104190
ISSN: 0022247X
DOI: 10.1006/jmaa.2001.7479
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