On sampling theorem with sparse decimated samples

The classical sampling Nyquist-Shannon-Kotelnikov theorem states that a band-limited continuous time function is uniquely defined by infinite two-sided sampling series taken with a sufficient frequency. The paper shows that these band-limited functions allows an arbitrarily close uniform approximation by functions that are uniquely defined by their extremely sparse subsamples representing arbitrarily small fractions of one-sided equidistant sample series with fixed oversampling parameter. In particular, an arbitrarily small adjustment of a band-limited underlying function makes redundant every (m-1) members of any set of m samples for an arbitrarily large m. This allows to bypass, in a certain sense, the restriction on the sampling rate defined by the critical Nyquist rate.