Geodesic
The system of shifts of functions
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 8 (2011), pp. 37-44

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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 $L^{2}\left(\mathbb{R}\right)$.
Keywords: Bessel sequence, frame, shift operator, complete systems. 
@article{VSGU_2011_8_a3,
     author = {E. S. Klimova},
     title = {The system of shifts of functions},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {37--44},
     publisher = {mathdoc},
     number = {8},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2011_8_a3/}
}
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E. S. Klimova. The system of shifts of functions. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 8 (2011), pp. 37-44. http://geodesic.mathdoc.fr/item/VSGU_2011_8_a3/