Geodesic
Finitely Generated Submodules in the Module of Entire Functions Determined by Restrictions on the Indicator Function
Matematičeskie zametki, Tome 71 (2002) no. 1, pp. 3-17

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We study finitely generated submodules in the module $P$ of entire functions bounded by a system of $\rho$-trigonometrically convex weights majorized by a given $\rho$-trigonometrically convex function. Sufficient conditions for the ampleness of a finitely generated submodule in terms of the relative position of the zeros of its generators are obtained. Using these conditions, we prove that each ample submodule in $P$ is generated by two (possibly, coinciding) functions. 
@article{MZM_2002_71_1_a0,
     author = {N. F. Abuzyarova},
     title = {Finitely {Generated} {Submodules} in the {Module} of {Entire} {Functions} {Determined} by {Restrictions} on the {Indicator} {Function}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
     volume = {71},
     number = {1},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a0/}
}
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N. F. Abuzyarova. Finitely Generated Submodules in the Module of Entire Functions Determined by Restrictions on the Indicator Function. Matematičeskie zametki, Tome 71 (2002) no. 1, pp. 3-17. http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a0/