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Mat. Zametki, 2002, Volume 71, Issue 1, Pages 3–17 (Mi mz323)  

This article is cited in 4 scientific papers (total in 4 papers)

Finitely Generated Submodules in the Module of Entire Functions Determined by Restrictions on the Indicator Function

N. F. Abuzyarova

Bashkir State University

Abstract: 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.

DOI: https://doi.org/10.4213/mzm323

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English version:
Mathematical Notes, 2002, 71:1, 3–16

Bibliographic databases:

UDC: 517.53
Received: 27.01.2000
Revised: 15.02.2001

Citation: N. F. Abuzyarova, “Finitely Generated Submodules in the Module of Entire Functions Determined by Restrictions on the Indicator Function”, Mat. Zametki, 71:1 (2002), 3–17; Math. Notes, 71:1 (2002), 3–16

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. B. N. Khabibullin, “Closed Submodules of Holomorphic Functions with Two Generators”, Funct. Anal. Appl., 38:1 (2004), 52–64  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. B. N. Khabibullin, “Spectral synthesis for the intersection of invariant subspaces of holomorphic functions”, Sb. Math., 196:3 (2005), 423–445  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. N. F. Abuzyarova, “Closed submodules in the module of entire functions of exponential type and polynomial growth on the real axis”, Ufa Math. J., 6:4 (2014), 3–17  mathnet  crossref
    4. 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 Math. J., 8:3 (2016), 8–21  mathnet  crossref  mathscinet  isi  elib
  • Математические заметки Mathematical Notes
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