On the system $\{f(\lambda_{j}z)\}$ series

The aim of the paper is to search the conditions of the expansion of the functions analytical in a unit circle in a series of the $\sum\limits_{j=1}^{\infty}d_{j}f(\lambda_{j}z)$ kind, where $f(z)$ is the function analytical in a unit circle, $|\lambda_{j}|<1$. The proved theorems contain as a special case the well-known results about the expansion of analytical functions in the rational series of the form $\sum\limits_{j=1}^{\infty}\frac{d_{j}}{1-\lambda_{j}z}$.