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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. Khabibullinab

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)
References:
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.
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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  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Функциональный анализ и его приложения Functional Analysis and Its Applications
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