The system of shifts of functions

The system of shift of functions $\left(T_{\lambda _{k}}g\left(x\right)\right)_{n\in \mathbb{Z}}$ in $L^{2}\left(\mathbb{R}\right)$ space is considered in this paper, where $\lambda_{n}\in \mathbb{R}$. We find conditions on real sequence $\left(\lambda_{n}\right)$ which provide such properties of the system as to be a frame, Bessel system, complete sequence in the space $L^{2}\left(\mathbb{R}\right)$.