Interpolation of infinite order entire functions (Q1344575)

The author considers spaces of entire functions which grow roughly like \(\exp (\exp |z|^\alpha)\) and show that the interpolation theorems proved in [The reviewer and \textit{B. A. Taylor}, Adv. Math. 33, 109-143 (1979; Zbl 0432.30028)] and [\textit{W. A. Squires}, Trans. Am. Math. Soc. 280, 401-423 (1983; Zbl 0549.30025)] for functions of finite order extend to this case. There has been some further progress in interpolation since this paper was written. In joint work of the reviewer and B. Q. Li, to appear shortly in J. Geom. Anal., geometric necessary and sufficient conditions for interpolation are derived, see also [the reviewer and \textit{Bao Qin Li} and \textit{A. Vidras}, Can. J. Math. 47, No. 1, 28-43 (1995; Zbl 0827.30014)].