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},
pages = {3--17},
publisher = {mathdoc},
volume = {71},
number = {1},
year = {2002},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a0/}
}
TY - JOUR AU - N. F. Abuzyarova TI - Finitely Generated Submodules in the Module of Entire Functions Determined by Restrictions on the Indicator Function JO - Matematičeskie zametki PY - 2002 SP - 3 EP - 17 VL - 71 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a0/ LA - ru ID - MZM_2002_71_1_a0 ER -
%0 Journal Article %A N. F. Abuzyarova %T Finitely Generated Submodules in the Module of Entire Functions Determined by Restrictions on the Indicator Function %J Matematičeskie zametki %D 2002 %P 3-17 %V 71 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a0/ %G ru %F MZM_2002_71_1_a0
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/