Abstract
We demonstrate that if a sequence of positive numbers increasing to infinity has S-density then it can be prolonged to some sequence that is the zero set of the Weierstrass product of regular behavior on the real axis.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 5, pp. 995–1007, September–October, 2007.
Original Russian Text Copyright © 2007 Gaĭsin A. M. and Sergeeva D. I.
The authors were supported by the Russian Foundation for Basic Research (Grant 05-01-00417-a).
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Gaisin, A.M., Sergeeva, D.I. Entire functions with a given sequence of zeros and of regular behavior on the real axis. I. Sib Math J 48, 798–808 (2007). https://doi.org/10.1007/s11202-007-0082-5
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DOI: https://doi.org/10.1007/s11202-007-0082-5