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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
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
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
Linking options:
https://www.mathnet.ru/eng/ufa256https://doi.org/10.13108/2014-6-4-3 https://www.mathnet.ru/eng/ufa/v6/i4/p3
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Abstract page: | 422 | Russian version PDF: | 134 | English version PDF: | 12 | References: | 59 |
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