Geodesic
The system of weighted exponentials with power weights
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 2 (2011), pp. 15-25 Cet article a éte moissonné depuis la source Math-Net.Ru

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The system of weighted exponentials $\left(\mid x\mid ^{\alpha }\exp^{i\lambda _{n}x}\right)_{n\in \mathbb{Z}}$ with power weights is considered in this paper, where $\lambda_{n}\in \mathbb{R}$. We find conditions on power indicator $\alpha$ which provide such properties of the system as to be a frame, Bessel system, Schauder basis in the space $L^{2}[-\pi ,\pi ]$.
Keywords: Bessel sequence, frame, system of weighted exponentials, complete systems. 
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     author = {E. S. Golubeva},
     title = {The system of weighted exponentials with power weights},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {15--25},
     year = {2011},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2011_2_a1/}
}
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E. S. Golubeva. The system of weighted exponentials with power weights. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 2 (2011), pp. 15-25. http://geodesic.mathdoc.fr/item/VSGU_2011_2_a1/

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