Geodesic
Closed submodules in the module of entire functions of exponential type and polynomial growth on the real axis
Ufa mathematical journal, Tome 6 (2014) no. 4, pp. 3-17

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In the work we consider a topological module $\mathcal P$ of entire functions, which is the isomorphic image under the Fourier–Laplace transform of Schwarz space $\mathcal E'$ of distributions compactly supported in a finite or infinite interval $(a;b)\subset\mathbb R$. We study some properties of closed submodules in module $\mathcal P$ related with local description problem. We also study issues on duality between closed submodules in $\mathcal P$ and subspaces in the space $\mathcal E=C^\infty(a;b)$ invariant w.r.t. the differentiation.
Keywords: entire functions, local description of submodules, invariant subspaces, spectral synthesis, finitely generated submodules.
Mots-clés : Fourier–Laplace transform 
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     author = {N. F. Abuzyarova},
     title = {Closed submodules in the module of entire functions of exponential type and polynomial growth on the real axis},
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N. F. Abuzyarova. Closed submodules in the module of entire functions of exponential type and polynomial growth on the real axis. Ufa mathematical journal, Tome 6 (2014) no. 4, pp. 3-17. http://geodesic.mathdoc.fr/item/UFA_2014_6_4_a0/