Localization of trigonometric polynomials and the Lev-Tselishchev lemma

The paper shows that the localization lemma used by N. Lev and A. Tselishchev in solving the problem of constructing quasi-bases from uniformly separated shifts of a function in the space $L^p(\mathbb{R})$ for $p>(1+\sqrt{5})\mathrm{/}2$, is not carried over to small $p$.