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Ufimsk. Mat. Zh., 2014, Volume 6, Issue 4, Pages 3–18 (Mi ufa256)  

This article is cited in 3 scientific papers (total in 3 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

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.

Full text: PDF file (689 kB)
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English version:
Ufa Mathematical Journal, 2014, 6:4, 3–17 (PDF, 473 kB); https://doi.org/10.13108/2014-6-4-3

Document Type: Article
UDC: 517.538.2+517.984.26+517.547
MSC: 30D15, 30H99, 42A38, 47E05
Received: 16.05.2014

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{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928228800}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. F. Abuzyarova, “Some properties of principal submodules in the module of entire functions of exponential type and polynomial growth on the real axis”, Ufa Math. J., 8:1 (2016), 1–12  mathnet  crossref  isi  elib
    2. 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
    3. N. F. Abuzyarova, “Spectral Synthesis for the Differentiation Operator in the Schwartz Space”, Math. Notes, 102:2 (2017), 137–148  mathnet  crossref  crossref  mathscinet  isi  elib
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