Article
Ufa Mathematical Journal
Volume 8, Number 1, pp. 3-12
Some properties of principal submodules in the module of entire functions of exponential type and polynomial growth on the real axis
Abuzyarova N.F.
DOI:10.13108/2016-8-1-3
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In the work we consider a topological module of entire functions $\mathcal P (a;b)$, which is the isomorphic image of Fourier-Laplace transform of Schwarz space formed by distributions with compact supports in a finite or infinite segment $(a;b)\subset\mathds{R}$. We study the conditions ensuring that the principal submodule of module $\mathcal P(a;b)$ can be uniquely recovered by the zeroes of a generating function.