On the perturbations of maps obeying Shannon–Whittaker–Kotel’nikov’s theorem generalization

Abstract

AbstractLet $f: \mathbb{R}\rightarrow \mathbb{R}$ f : R → R be a map and $\tau \in \mathbb{R}^{+}$ τ ∈ R + . The map f obeys the Shannon–Whittaker–Kotel’nikov theorem generalization (SWKTG) if $f(t)=\lim_{n\to \infty } ( \sum_{k\in \mathbb{Z}} f^{ \frac{1}{n}} (\frac{k}{\tau } ) \operatorname{sinc} (\tau t-k) )^{n}$ f ( t ) = lim n → ∞ ( ∑ k ∈ Z f 1 n ( k τ ) sinc ( τ t − k ) ) n for every $t\in \mathbb{R}$ t ∈ R . The aim of the present paper is to characterize the perturbations of the map f that obeys SWKTG. Our results enlarge the catalog of maps that can be recomposed using SWKTG. We underline that maps obeying SWKTG play a central role in applications to chemistry and signal theory between other fields.