Shannon-Nyquist-like condition derived from other principles

In this paper, we report on two important results within the mathematical theory of analog signal sampling that we obtained recently. First, we demonstrate that in order for a comb of impulses to correctly describe a sampled signal in the domain of a continuous time, the pulses of which it is composed must be pulses of a finite duration. Second, it is shown that a condition similar to the well-known Shannon-Nyquist sampling criterion for a perfect signal recovery can be derived using some other principles.