This article is cited in 8 papers

Entire functions with a given sequence of zeros and of regular behavior on the real axis. I

A. M. Gaisin, D. I. Sergeeva

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

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.

Keywords: Weierstrass product, Cartwright class.

UDC: 517.53

Received: 30.05.2005
Revised: 14.11.2006

 English version: Siberian Mathematical Journal, 2007, 48:5, 798–808

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