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Stability of the Shifts of Global Supported Distributions

โœ Scribed by Qiyu Sun

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
121 KB
Volume
261
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

For a tempered distribution with l l 1 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 l l 1 decay has stable shifts, then we can recover all distributions in V , the space of all linear combinations of its shifts ฯฑ using bounded sequences, in a stable way using C ฯฑ dual functions with l l 1 decay at infinity. If, additionally, that tempered distribution is compactly supported, then the above C ฯฑ dual functions can be chosen to have exponential decay at infinity.

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