Geodesic
On absolute completeness of systems of exponentials on a closed interval
Sbornik. Mathematics, Tome 59 (1988) no. 2, pp. 303-315 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $\Lambda=\{\lambda_i\}$ be a sequence of points in the complex plane, and $M=\{m_i\}$ a sequence of positive numbers. Problem: under what relations between $\Lambda$ and $M$ can any function in $C[a,b]$ be approximated in the uniform norm by finite linear combinations $\sum a_ie^{\lambda_ix}$ of exponentials with the coefficient restriction $|a_i|\leqslant C_fm_i$. Here $C_f$ depends only on $f$. An exact solution of the problem is given under the assumption that $\big|\frac{\operatorname{Im}\lambda_i}{\operatorname{Re}\lambda_i}\big|\leqslant\text{Const}$. Bibliography: 26 titles. 
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I. F. Krasichkov-Ternovskii. On absolute completeness of systems of exponentials on a closed interval. Sbornik. Mathematics, Tome 59 (1988) no. 2, pp. 303-315. http://geodesic.mathdoc.fr/item/SM_1988_59_2_a2/

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