N. F. Abuzyarova, “Spectral Synthesis for the Differentiation Operator in the Schwartz Space”, Mat. Zametki, 102:2 (2017), 163–177; Math. Notes, 102:2 (2017), 137

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Matematicheskie Zametki, 2017, Volume 102, Issue 2, Pages 163–177
DOI: https://doi.org/10.4213/mzm11218 (Mi mzm11218)

This article is cited in 15 scientific papers (total in 15 papers)

Spectral Synthesis for the Differentiation Operator in the Schwartz Space

N. F. Abuzyarova

Bashkir State University, Ufa

Full-text PDF (552 kB) Citations (15)

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DOI: https://doi.org/10.4213/mzm11218

Abstract: We consider the spectral synthesis problem for the differentiation operator on the space of infinitely differentiable functions on a finite or infinite interval of the real line and the dual problem of local description of closed submodules in a special module of entire functions.

Keywords: invariant subspace, weak spectral synthesis, exponential monomial, Fourier–Laplace transform, local description of submodules.

Funding agency	Grant number
Ministry of Education and Science of the Russian Federation	01201456408
This work was supported by the Ministry of Education and Science of the Russian Federation (grant no. 01201456408).

Received: 03.05.2016

English version:
Mathematical Notes, 2017, Volume 102, Issue 2, Pages 137–148
DOI: https://doi.org/10.1134/S0001434617070161

Bibliographic databases:

Document Type: Article

UDC: 517.538.2+517.984.26+517.518.83+517.547.2

Language: Russian

Citation: N. F. Abuzyarova, “Spectral Synthesis for the Differentiation Operator in the Schwartz Space”, Mat. Zametki, 102:2 (2017), 163–177; Math. Notes, 102:2 (2017), 137–148

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Linking options:

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https://doi.org/10.4213/mzm11218

https://www.mathnet.ru/eng/mzm/v102/i2/p163

This publication is cited in the following 15 articles:

N. F. Abuzyarova, Z. Yu. Fazullin, “Invariant subspaces in non-quasianalytic spaces of $\Omega$ -ultradifferentiable functions on an interval”, Eurasian Math. J., 15:3 (2024), 9–24
N. F. Abuzyarova, “Invariantnye podprostranstva v nekvazianaliticheskikh prostranstvakh $\Omega$ -ultradifferentsiruemykh funktsii na intervale”, Izv. vuzov. Matem., 2023, no. 11, 86–91
N. F. Abuzyarova, “Invariant Subspaces in Nonquasianalytic Spaces of Ω-Ultradifferentiable Functions on an Interval”, Russ Math., 67:11 (2023), 75
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, “On condition of representing a subspace in Schwartz space invariant with respect to differentiation as direct sum of its residual and exponential components”, Ufa Math. J., 13:4 (2021), 3–7
N. F. Abuzyarova, “On conditions of invertibility in the sense of Ehrenpreis in the Schwartz algebra”, Lobachevskii J. Math., 42:6, SI (2021), 1141–1153
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, “On Shifts of the Sequence of Integers Generating Functions that are Invertible in the Sense of Ehrenpreis”, J Math Sci, 251:2 (2020), 161
A. Baranov, Yu. Belov, “Synthesizable differentiation-invariant subspaces”, Geom. Funct. Anal., 29:1 (2019), 44–71
N. F. Abuzyarova, “Functions in the Schwartz algebra that are invertible in the sense of Ehrenpreis”, Dokl. Math., 99:1 (2019), 1–4
N. F. Abuzyarova, “O sdvigakh tselochislennoi posledovatelnosti, porozhdayuschikh funktsii, obratimye po Erenpraisu”, Issledovaniya po lineinym operatoram i teorii funktsii. 47, Zap. nauchn. sem. POMI, 480, POMI, SPb., 2019, 5–25

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

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