In this paper we consider the Schwartz module of entire functions of exponential type having polynomial growth along the real axis. This module is equipped with the non-metrizable locally convex topology. We establish that any principal submodule is the set of limits of converging sequences which members are polynomials multiplied by the generator of the submodule. We also obtain a weight weak localizability criterion for principal submodules and some results concerning the notion «synthesizable sequence» recently introduced by A. Baranov and Yu. Belov.

中文翻译：

---

Schwartz模块中的主要子模块

在本文中，我们考虑了具有沿实轴的多项式增长的指数型整体函数的Schwartz模块。该模块配备了不可度量的局部凸形拓扑。我们确定，任何主要子模块都是收敛序列的极限集合，其成员是多项式乘以子模块的生成器。我们还获得了主要子模块的权重弱可定位性准则，以及有关A. Baranov和Yu最近引入的“可合成序列”概念的一些结果。贝洛夫。