Series in the system $\{f(nx)\}_{n=1}^\infty$

This article studies questions of convergence of operators commuting with ergodic endomorphisms, as well as convergence of function series of the form $\sum a_nf(nx)$, where $\{n\}_{n=1}^\infty$ is the sequence of positive integers, $x\in[0,1]$, and $f(x+1)=f(x)$, and series of the form $\sum a_nf(\tau^nx)$, where $\tau$ is an ergodic endomorphism of some algebra $G$, and $f\in L_2(G)$.
Bibliography: 13 titles.