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Matematicheskie Zametki, 2002, Volume 71, Issue 1, Pages 3–17
DOI: https://doi.org/10.4213/mzm323 (Mi mzm323) 		 
This article is cited in 5 scientific papers (total in 5 papers)

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

N. F. Abuzyarova

Bashkir State University
Full-text PDF (236 kB) Citations (5)
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DOI: https://doi.org/10.4213/mzm323
Abstract: We study finitely generated submodules in the module P of entire functions bounded by a system of ρ-trigonometrically convex weights majorized by a given ρ-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.
Received: 27.01.2000
Revised: 15.02.2001
English version:
Mathematical Notes, 2002, Volume 71, Issue 1, Pages 3–16
DOI: https://doi.org/10.1023/A:1013944304722
Bibliographic databases:
UDC: 517.53
Language: Russian
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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    • This publication is cited in the following 5 articles:
    1. 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
    2. 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
    3. Markov Processes, Semigroups and Generators, 2010, 403  crossref
    4. 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
    5. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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