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Interpolation of infinite order entire functions. (English) Zbl 0874.30028

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 B. A. Taylor, Adv. Math. 33, 109-143 (1979; Zbl 0432.30028)] and [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 Bao Qin Li and A. Vidras, Can. J. Math. 47, No. 1, 28-43 (1995; Zbl 0827.30014)].

MSC:

30E05 Moment problems and interpolation problems in the complex plane
41A05 Interpolation in approximation theory
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