Some properties of principal submodules in the module of entire functions of exponential type and polynomial growth on the real axis

Abstract

In the work we consider a topological module of entire functions P(a; b), which is the isomorphic image of Fourier-Laplace transform of Schwarz space formed by distributions with compact supports in a finite or infinite segment (a; b) ⊂ R. We study the conditions ensuring that the principal submodule of module P(a; b) can be uniquely recovered by the zeroes of a generating function.