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Entire functions with a given sequence of zeros and of regular behavior on the real axis. I. (Russian, English) Zbl 1164.30377

Sib. Mat. Zh. 48, No. 5, 995-1007 (2007); translation in Sib. Math. J. 48, No. 5, 798-808 (2007).
Summary: We demonstrate that if a sequence of positive numbers increasing to infinity has \(S\)-density then it can be extended to some sequence that is the zero set of a Weierstrass product of regular behavior on the real axis.

MSC:

30D15 Special classes of entire functions of one complex variable and growth estimates
30E10 Approximation in the complex plane
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