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Funktsional. Anal. i Prilozhen., 2004, Volume 38, Issue 1, Pages 65–80 (Mi faa97)  

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

Closed Submodules of Holomorphic Functions with Two Generators

B. N. Khabibullinab

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

Abstract: Let $I$ 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 $I$ is generated by two functions or two special submodules. As a corollary, it follows from these results that if an invariant subspace $W\subset C^{\infty}(a,b)$ (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

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

Full text: PDF file (266 kB)
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English version:
Functional Analysis and Its Applications, 2004, 38:1, 52–64

Bibliographic databases:

UDC: 517.98+517.53
Received: 04.07.2002

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

    This publication is cited in the following articles:
    1. B. N. Khabibullin, “Spectral synthesis for the intersection of invariant subspaces of holomorphic functions”, Sb. Math., 196:3 (2005), 423–445  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Gudkova E.V., “Finite reductions of the two dimensional Toda chain”, J. Nonlinear Math. Phys., 12, suppl. 2 (2005), 197–205  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. B. N. Khabibullin, “Dva obschikh usloviya nedopustimosti spektralnogo sinteza dlya invariantnykh podprostranstv golomorfnykh funktsii”, Vladikavk. matem. zhurn., 7:3 (2005), 71–78  mathnet  mathscinet  elib
    4. 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.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. 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  mathnet  crossref
    6. Abuzyarova N.F., “Spectral Synthesis in the Schwartz Space of Infinitely Differentiable Functions”, Dokl. Math., 90:1 (2014), 479–482  crossref  mathscinet  zmath  isi  scopus
    7. 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  mathnet  crossref  mathscinet  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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