Incomplete sampling series and the recovery of missing samples from oversampled band-limited signals

It is well known that a band-limited oversampled signal is completely determined even if an arbitrary finite number of samples is lost. It is shown that an alternative simple proof of this fact carries over to generalized sampling expansions. More precisely, it is shown that any finite number of missing samples can be recovered from the remaining ones, in the case of generalized Kramer sampling expansions, if an appropriate oversampling constraint is satisfied. The recovery can be accomplished either iteratively or noniteratively