Gaĭsin, A. M.; Sergeeva, D. I. 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. Cited in 7 Documents MSC: 30D15 Special classes of entire functions of one complex variable and growth estimates 30E10 Approximation in the complex plane Keywords:Weierstrass product; Cartwright class PDFBibTeX XMLCite \textit{A. M. Gaĭsin} and \textit{D. I. Sergeeva}, Sib. Mat. Zh. 48, No. 5, 995--1007 (2007; Zbl 1164.30377); translation in Sib. Math. J. 48, No. 5, 798--808 (2007) Full Text: EuDML EMIS