Geodesic
On $2$-generateness of weakly localizable submodules in the module of entire functions of exponential type and polynomial growth on the real axis
Ufa mathematical journal, Tome 8 (2016) no. 3, pp. 8-21

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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.
Keywords: entire functions, subharmonic functions, finitely generated submodules, description of submodules, local description of submodules, invariant subspaces, spectral synthesis.
Mots-clés : Fourier–Laplace transform 
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     author = {N. F. Abuzyarova},
     title = {On $2$-generateness of weakly localizable submodules in the module of entire functions of exponential type and polynomial growth on the real axis},
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N. F. Abuzyarova. On $2$-generateness of weakly localizable submodules in the module of entire functions of exponential type and polynomial growth on the real axis. Ufa mathematical journal, Tome 8 (2016) no. 3, pp. 8-21. http://geodesic.mathdoc.fr/item/UFA_2016_8_3_a2/