Geodesic
On the closure of nonclosed systems of functions of Mittag-Leffler type
Izvestiya. Mathematics, Tome 10 (1976) no. 1, pp. 93-110 
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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     title = {On the closure of nonclosed systems of functions of {Mittag-Leffler} type},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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[4] Koosis P., “Interior compact spaces of functions on a half-line”, Comm. Pure Appl. Math., X:4 (1957), 583–615 | DOI | MR

[5] Lax P. D., “Remarks on the preceding paper”, Comm. Pure Appl. Math., X:4 (1957), 617–622 | DOI | MR

[6] Dzhrbashyan M. M., “O vypolnenii i zamykanii nepolnoi sistemy funktsii $\{e^{-\mu}k^xx^sk^{-1}\}$”, Dokl. AN SSSR, 141:3 (1961), 539–542 | Zbl

[7] Dzhrbashyan M. M., “O zamknutosti sistem funktsii tipa Mittag–Lefflera”, Dokl. AN SSSR, 219:6 (1974), 1302–1305 | Zbl

[8] Dzhrbashyan M. M., Integralnye preobrazovaniya i predstavleniya funktsii v kompleksnoi oblasti, Nauka, M., 1966

[9] Dzhrbashyan M. M., Avetisyan A. E., “Integralnoe predstavlenie nekotorykh klassov funktsii, analiticheskikh v oblasti ugla”, Sib. matem. zh., 1:3 (1960), 383–426 | MR | Zbl

[10] Dzhrbashyan M. M., “O popolnenii nepolnoi sistemy Malmkvista na veschestvennoi osi”, Dokl. AN ArmSSR, 35:2 (1962), 55–61 | Zbl

[11] Tumarkin G. Ts., “Opisanie klassa funktsii, dopuskayuschikh priblizhenie drobyami s fiksirovannymi polyusami”, Izv. AN ArmSSR. Matematika, I:2 (1966), 89–105 | MR

[12] Uitteker E. T., Vatson Dzh. N., Kurs sovremennogo analiza, t. I, Fizmatgiz, M., 1963

[13] Khachatryan I. O., “O polnote semeistv funktsii tipa Mittag–Lefflera pri vzveshenno- ravnomernom priblizhenii v kompleksnoi oblasti”, Matem. zametki, 18:5 (1975), 675–685 | MR | Zbl

[14] Akopyan S. A., “Teorema o dvukh postoyannykh dlya funktsii klassa $H_p$”, Izv. AN ArmSSR. Matematika, 2:2 (1967), 123–127 | MR | Zbl

[15] Musoyan V. X., “O lakunarnykh sistemakh Dirikhle”, Izv. AN ArmSSR. Matematika, VII:2 (1972), 104–112

[16] Musoyan V. X., “O sistemakh Dirikhle na proizvolnykh mnozhestvakh”, Izv. AN ArmSSR. Matematika, IX:2 (1974), 121–134