# Article

Ufa Mathematical Journal
Volume 6, Number 4, pp. 3-17

# Closed submodules in the module of entire functions of exponential type and polynomial growth on the real axis

Abuzyarova N.F.

DOI:10.13108/2014-6-4-3

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 $(a;b)\subset\mathds{R}$. 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.