On some representing systems in spaces of analytic functions

Yu. F. Korobeinik

Izvestiya. Mathematics , Tome 23 (1984) no. 3, pp. 487-509

Résumé

Let $E_\rho(z)$ be the Mittag-Leffler function. This article investigates the connection between “representing” properties for systems $\mathscr E_{\rho,\Lambda}=\{E_{\rho}(\lambda_kz)\}^{\infty}_{k=1}$ and $\mathscr E^{(n)}_{\rho,\Lambda}=\{E_\rho(\lambda_kz),zE_\rho(\lambda_kz),\dots,z^nE_\rho(\lambda_kz)\}^{\infty}_{k=1}$, $n\geqslant1$, as well as for systems $\mathscr E^1_{\rho,\Lambda}=\{E_\rho(\lambda_{k,1}z)\}^\infty_{k=1}$, $\mathscr E^2_{\rho,\Lambda}=\{E_\rho(\lambda_{k,2}z)\}^\infty_{k=1}$, and $\mathscr E^3_{\rho,\Lambda}=\mathscr E^1_{\rho,\Lambda}\cup\mathscr E^2_{\rho,\Lambda}$ in spaces of analytic functions. Bibliography: 18 titles.