The multiple interpolation problem in the space of entire functions of given proximate order

A. V. Bratishchev ; Yu. F. Korobeinik

Izvestiya. Mathematics , Tome 10 (1976) no. 5, pp. 1049-1074

Résumé

In this paper criteria are obtained for solvability of the multiple interpolation problem in the class $[\rho(r),\infty)$, where $\rho(r)$ is a proximate order ($\lim_{r\to\infty}\rho(r)=\rho$, $0\leqslant\rho\infty$) for any sequence from a certain class $\textit Л_{\rho(r)}$ or one of its subclasses. The results are applied to find criteria that the system $\{z^{l-1}\exp\lambda_nz$, $l=1,\dots, p_n\}^\infty_{n=1}$ be a basis in its linear hull. Bibliography: 14 titles.