Abstract :
For a tempered distribution with 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 1 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 l 1 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.
