Geodesic
Approximation properties of exponential systems on the real line and the half-line
Sbornik. Mathematics, Tome 189 (1998) no. 3, pp. 443-460 Cet article a éte moissonné depuis la source Math-Net.Ru

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For arbitrary $a>0$ and $\alpha >1$ a class of entire functions depending on a complex parameter $\mu$ is constructed. The values of $\mu$ such that the sequence of zeros $\lambda _n$ of a function in this class generates a complete and minimal exponential system $$ \exp \bigl (-i\lambda _nt-a|t|^\alpha \bigr) $$ in $L^p(\mathbb R)$ $(L^p(\mathbb R_+))$, $p\geqslant 2$, are described. Examples of such systems were previously known only for $\alpha=2$. 
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A. M. Sedletskii. Approximation properties of exponential systems on the real line and the half-line. Sbornik. Mathematics, Tome 189 (1998) no. 3, pp. 443-460. http://geodesic.mathdoc.fr/item/SM_1998_189_3_a5/

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