Recovery of missing samples for oversampling in shift invariant spaces

It is well known that any finite missing samples of a band-limited signal can be recovered from the remaining known samples when the signal is oversampled at a rate higher than the minimum Nyquist rate. We consider a similar problem for oversampled signals in shift invariant spaces with compactly supported continuous Riesz generators. Using a multi-channel oversampling, we find conditions under which finitely many missing samples can be recovered.