On a description of bases of generalized systems of exponentials

All bases of the form $\{f(\lambda_nz)\}$ are described for the space $A_R$. In particular, it is shown that for a given entire function $f$ there exists a countable set $\{\lambda_n\}$ such that the system $\{f(\lambda_nz)\}$ forms a basis in $A_R$, $0<R<\infty$ if and only if $f_n\ne0$ for all $n$, $\lim\limits_{n\to\infty}|\hat f_n/f_n|^{1/n}=1$ and $(\exists\,\sigma>1)(\exists\,\sigma_1>1)(\forall\,k\geqslant1)(\forall\,m\geqslant k)$: $\varkappa_k/\varkappa_m\leqslant\sigma_1^k/\sigma^m$ where $\varkappa_n=|f_{n-1}/f_n|$, $\hat f$ is the Newton majorant of the function $f$, and $f_n=f^{(n)}(0)/n!$ .
Bibliography: 20 titles.