This article is cited in 1 paper

On the closure of nonclosed systems of functions of Mittag-Leffler type

S. A. Akopyan, I. O. Khachatryan


Abstract: 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.

UDC: 517.5

MSC: Primary 30A18; Secondary 44A10

Received: 24.01.1975

 English version: Mathematics of the USSR-Izvestiya, 1976, 10:1, 93–110

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