Abstract:
In the work we consider a topological module P of entire functions, which is the isomorphic image under the Fourier–Laplace transform of Schwarz space E′ of distributions compactly supported in a finite or infinite interval (a;b)⊂R. We study some properties of closed submodules in module P related with local description problem. We also study issues on duality between closed submodules in P and subspaces in the space E=C∞(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.
Citation:
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
\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 Ufa Math. J.
\yr 2014
\vol 6
\issue 4
\pages 3--17
\mathnet{http://mi.mathnet.ru/eng/ufa256}
\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:
N. F. Abuzyarova, “Representation of invariant subspaces of the Schwartz space”, Sb. Math., 213:8 (2022), 1020–1040
N. F. Abuzyarova, “Differentiation Operator in the Beurling Space of Ultradifferentiable Functions of Normal Type on an Interval”, Lobachevskii J Math, 43:6 (2022), 1472
N. F. Abuzyarova, “Preserving certain classes of entire functions defined by growth restrictions along the real axis under perturbations of their zero sets”, St. Petersburg Math. J., 33:4 (2022), 585–606
N. F. Abuzyarova, “Principal submodules in the Schwartz module”, Russian Math. (Iz. VUZ), 64:5 (2020), 74–78
N. F. Abuzyarova, A. F. Sagadieva, Z. Yu. Fazullin, “O nulevykh mnozhestvakh slabo lokalizuemykh glavnykh podmodulei v algebre Shvartsa”, Chelyab. fiz.-matem. zhurn., 5:3 (2020), 261–270
N. F. Abuzyarova, “Synthesizable sequence and principle submodules in Schwartz module”, Ufa Math. J., 12:3 (2020), 11–21
N. F. Abuzyarova, “Spectral Synthesis for the Differentiation Operator in the Schwartz Space”, Math. Notes, 102:2 (2017), 137–148
N. F. Abuzyarova, “Principal submodules in the module of entire functions, which is dual to the Schwartz space, and weak spectral synthesis in the Schwartz space”, J. Math. Sci. (N. Y.), 241:6 (2019), 658–671
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
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
Citation in format AMSBIB
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