On the completeness and quasipower basis property of systems $\{z^nf(\lambda_nz)\}$

This paper discusses questions of completeness and the quasipower property in spaces $A_R$ of systems of functions $\{z^nf(\lambda_nz)\}$ under some natural conditions on the Taylor coefficients of the function $f(z)$, assumed regular in a disk $|z|<r\in(0,+\infty]$. The complex numbers $\lambda_n$ ($n=0,1,\dots$) are subject to the condition $|\lambda_n|\leqslant1$.
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