Finitely generated submodules in the module of entire functions that is determined by restrictions on the indicator. (Q1810044)

Let \(P\) be a module of entire functions in \(C\) of order not greater than \(\rho >0\), whose indicator functions do not exceed a given \(\rho\)-trigonometrically convex function. Such modules were studied in detail by \textit{I. Krasichkov-Ternovskii} [see, e.g., Math. USSR-Sb., Vol. 181, No. 12, 1640--1658 (1990; Zbl 0776.30034), and the references therein]. The present author studies finitely generated submodules in \(P\). She proves that any ample (i.e., completely defined by the zeros of its functions) submodule has two generators.