Geodesic
On the closure of nonclosed systems of functions of Mittag-Leffler type
Izvestiya. Mathematics , Tome 10 (1976) no. 1, pp. 93-110.

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The closure of a system of functions of Mittag-Leffler type $\{E_\rho(-\lambda_kx;\mu)\}_1^\infty$ ($\operatorname{Re}\lambda_k^\alpha>0$, $1/\rho+1/\alpha=2$) is described in the space $L_{2,\omega}(0,+\infty)$ in the case when the series $$ \sum_{k=1}^\infty\frac{\operatorname{Re}\lambda_k^\alpha}{1+|\lambda_k|^{2\alpha}} $$ is convergent. This result generalizes the well-known theorems of Laurent Schwartz, A. F. Leont'ev and M. M. Dzhrbashyan. Bibliography: 16 titles. 
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S. A. Akopyan; I. O. Khachatryan. On the closure of nonclosed systems of functions of Mittag-Leffler type. Izvestiya. Mathematics , Tome 10 (1976) no. 1, pp. 93-110. http://geodesic.mathdoc.fr/item/IM2_1976_10_1_a5/

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