Sectorial Finitely Generated Dynamical Frames

We study frames of unilateral iterations generated by finitely many vectors under an invertible bounded operator $T$. Suppose that the spectrum of $T$ lies in $\{ρe^{it}:0<ρ\le1,\ |t|\le c\}$, where $c<π$, and that its essential spectrum lies in $\{e^{it}:|t|\le c_{\mathrm e}\}$, where $0\le c_{\mat