Geodesic
A necessary condition for the uniform minimality of a system of exponentials in $L^p$ spaces on the line
Sbornik. Mathematics, Tome 192 (2001) no. 11, pp. 1721-1740 Cet article a éte moissonné depuis la source Math-Net.Ru

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A necessary condition for the uniform minimality of a system of weighted exponentials $$ \exp(-i\lambda_nt-a|t|^\alpha), \qquad a>0, \quad \alpha >1, $$ is obtained in the spaces $L^p$ $(1\leqslant p<\infty)$ and $C_0$ on the real line and the half-line. This condition is stated in terms of the indicator of the entire function of order $\beta=\alpha/(\alpha-1)$ with zero set coinciding with the sequence $\lambda_n$. This condition is used to show that there are no bases among the known complete minimal systems of this form in the above-indicated spaces. 
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A. M. Sedletskii. A necessary condition for the uniform minimality of a system of exponentials in $L^p$ spaces on the line. Sbornik. Mathematics, Tome 192 (2001) no. 11, pp. 1721-1740. http://geodesic.mathdoc.fr/item/SM_2001_192_11_a6/

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