B. N. Khabibullin, “Closed Submodules of Holomorphic Functions with Two Generators”, Funktsional. Anal. i Prilozhen., 38:1 (2004), 65–80; Funct. Anal. Appl., 38:1 (2004), 52

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Funktsional'nyi Analiz i ego Prilozheniya, 2004, Volume 38, Issue 1, Pages 65–80
DOI: https://doi.org/10.4213/faa97 (Mi faa97)

This article is cited in 7 scientific papers (total in 7 papers)

Closed Submodules of Holomorphic Functions with Two Generators

B. N. Khabibullin^ab

^a Bashkir State University
^b Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Full-text PDF (266 kB) Citations (7)

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DOI: https://doi.org/10.4213/faa97

Abstract: Let

I

$I$ be a closed submodule over a polynomial ring in a space of holomorphic functions on a domain in the complex plane. We establish sufficient conditions under which

I

$I$ is generated by two functions or two special submodules. As a corollary, it follows from these results that if an invariant subspace

W \subset C^{\infty} (a, b)

$W\subset C^{\infty}(a,b)$ (with respect to the differentiation operator) admits spectral synthesis, then it is the solution space of a system of two homogeneous convolution equations.

Keywords: spaces of holomorphic functions, module over the ring of polynomials, local description of closed submodules, finitely generated submodule, spectral synthesis, convolution equation.

Received: 04.07.2002

English version:
Functional Analysis and Its Applications, 2004, Volume 38, Issue 1, Pages 52–64
DOI: https://doi.org/10.1023/B:FAIA.0000024868.54361.8b

Bibliographic databases:

Document Type: Article

UDC: 517.98+517.53

Language: Russian

Citation: B. N. Khabibullin, “Closed Submodules of Holomorphic Functions with Two Generators”, Funktsional. Anal. i Prilozhen., 38:1 (2004), 65–80; Funct. Anal. Appl., 38:1 (2004), 52–64

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/faa97

https://doi.org/10.4213/faa97

https://www.mathnet.ru/eng/faa/v38/i1/p65

This publication is cited in the following 7 articles:

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
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
Abuzyarova N.F., “Spectral Synthesis in the Schwartz Space of Infinitely Differentiable Functions”, Dokl. Math., 90:1 (2014), 479–482
Gurses M., Habibullin I., Zheltukhin K., “Integrable boundary value problems for elliptic type Toda lattice in a disk”, J. Math. Phys., 48:10 (2007), 102702, 16 pp.
B. N. Khabibullin, “Spectral synthesis for the intersection of invariant subspaces of holomorphic functions”, Sb. Math., 196:3 (2005), 423–445
Gudkova E.V., “Finite reductions of the two dimensional Toda chain”, J. Nonlinear Math. Phys., 12, suppl. 2 (2005), 197–205
B. N. Khabibullin, “Dva obschikh usloviya nedopustimosti spektralnogo sinteza dlya invariantnykh podprostranstv golomorfnykh funktsii”, Vladikavk. matem. zhurn., 7:3 (2005), 71–78

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

Functional Analysis and Its Applications

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