On non-quasianalytic representations of Abelian groups

Анотація

We study representations $T_g$ of a locally compact Abelian group $G$ with a scattered spectrum satisfying the conditions: there exists $S\subset G$ such that $G=S-S$ and for all $s\in S$ $$||T_{ns}||=o(n^k), k\ge 1, \ln ||T_{-ns}||=o(\sqrt{n}), \textrm{ as } n\to +\infty .$$