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|Title:||Stability of the shifts of global supported distributions|
|Source:||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|
|Appears in Collections:||Staff Publications|
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