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

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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. 
@article{SM_2001_192_11_a6,
     author = {A. M. Sedletskii},
     title = {A~necessary condition for the uniform minimality of a~system of exponentials in~$L^p$ spaces on the line},
     journal = {Sbornik. Mathematics},
     pages = {1721--1740},
     publisher = {mathdoc},
     volume = {192},
     number = {11},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2001_192_11_a6/}
}
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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/