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Ufimsk. Mat. Zh., 2016, Volume 8, Issue 3, Pages 8–21 (Mi ufa322)  

On $2$-generateness of weakly localizable submodules in the module of entire functions of exponential type and polynomial growth on the real axis

N. F. Abuzyarova

Bashkir State University, Ufa

Abstract: In the work we consider a topological module $\mathcal P(a;b)$ of entire functions, which is the isomorphic image of the Schwarz space of distributions with compact supports in a finite or infinite interval $(a;b)\subset\mathbb R$ under the Fourier–Laplace transform. We prove that each weakly localizable module in $\mathcal P (a;b)$ is either generated by its two elements or is equal to the closure of two submodules of special form. We also provide dual results on subspaces in $C^\infty(a;b)$ invariant w.r.t. the differentiation operator.

Keywords: entire functions, subharmonic functions, Fourier–Laplace transform, finitely generated submodules, description of submodules, local description of submodules, invariant subspaces, spectral synthesis.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 01201456408


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English version:
Ufa Mathematical Journal, 2016, 8:3, 8–21 (PDF, 442 kB); https://doi.org/10.13108/2016-8-3-8

Bibliographic databases:

Document Type: Article
UDC: 517.538.2+517.984.26+517.547
MSC: 30D15, 30H99, 42A38, 47E05
Received: 31.05.2016

Citation: 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”, Ufimsk. Mat. Zh., 8:3 (2016), 8–21; Ufa Math. J., 8:3 (2016), 8–21

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