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Ufa Mathematical Journal, 2014, Volume 6, Issue 4, Pages 3–17
DOI: https://doi.org/10.13108/2014-6-4-3
(Mi ufa256)
 

This article is cited in 10 scientific papers (total in 10 papers)

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

N. F. Abuzyarova

Bashkir State University, Ufa, Russia
References:
Abstract: 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 $(a;b)\subset\mathbb R$. 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.
Keywords: entire functions, Fourier–Laplace transform, local description of submodules, invariant subspaces, spectral synthesis, finitely generated submodules.
Received: 16.05.2014
Russian version:
Ufimskii Matematicheskii Zhurnal, 2014, Volume 6, Issue 4, Pages 3–18
Bibliographic databases:
Document Type: Article
UDC: 517.538.2+517.984.26+517.547
Language: English
Original paper language: Russian
Citation: N. F. Abuzyarova, “Closed submodules in the module of entire functions of exponential type and polynomial growth on the real axis”, Ufimsk. Mat. Zh., 6:4 (2014), 3–18; Ufa Math. J., 6:4 (2014), 3–17
Citation in format AMSBIB
\Bibitem{Abu14}
\by N.~F.~Abuzyarova
\paper Closed submodules in the module of entire functions of exponential type and polynomial growth on the real axis
\jour Ufimsk. Mat. Zh.
\yr 2014
\vol 6
\issue 4
\pages 3--18
\mathnet{http://mi.mathnet.ru/ufa256}
\transl
\jour Ufa Math. J.
\yr 2014
\vol 6
\issue 4
\pages 3--17
\crossref{https://doi.org/10.13108/2014-6-4-3}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928228800}
Linking options:
  • https://www.mathnet.ru/eng/ufa256
  • https://doi.org/10.13108/2014-6-4-3
  • https://www.mathnet.ru/eng/ufa/v6/i4/p3
  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Уфимский математический журнал
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    Abstract page:422
    Russian version PDF:134
    English version PDF:12
    References:59
     
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