Article
Ufa Mathematical Journal
Volume 8, Number 3, pp. 8-21
On 2-generateness of weakly localizable submodules in the module of entire functions of exponential type and polynomial growth on the real axis
Abuzyarova N.F.
DOI:10.13108/2016-8-3-8
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In the work we consider a topological module $\mathcal P (a;b)$ of entire functions, which is the isomorphic image of the Schwarz space of distributions with compact supports in a finite or infinite interval $(a;b)\subset\mathbb R$ under the Fourier-Laplace transform. We prove that each weakly localizable module in
$\mathcal P (a;b)$ is either generated by its two elements or is equal to the closure of two submodules of special form. We also provide dual results on subspaces in $C^{\infty} (a;b)$ invariant w.r.t. the differentiation operator.