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 Mat. Sb., 2005, Volume 196, Number 3, Pages 119–142 (Mi msb1278)

Spectral synthesis for the intersection of invariant subspaces of holomorphic functions

B. N. Khabibullinab

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

Abstract: Let $\Omega$ be a convex domain in the complex plane $\mathbb C$ and $H$ the space of holomorphic functions in $\Omega$ with the topology of uniform convergence on compact subsets of $\Omega$. Let $W_1$ and $W_2$ be a pair of (differentiation) invariant subspaces of $H$ admitting spectral synthesis. Conditions ensuring that the intersection $W_1\cap W_2$ also admits spectral synthesis are described. One consequence of these conditions is a recent result of Abuzyarova (in a new, constructive and quantitative setting) on the representation of an invariant subspace admitting spectral synthesis as the solution space of a system of two homogeneous convolution equations.
New approximation results for entire functions of exponential type are used.

DOI: https://doi.org/10.4213/sm1278

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English version:
Sbornik: Mathematics, 2005, 196:3, 423–445

Bibliographic databases:

UDC: 517.982 + 517.53
MSC: 46E10, 30D99

Citation: B. N. Khabibullin, “Spectral synthesis for the intersection of invariant subspaces of holomorphic functions”, Mat. Sb., 196:3 (2005), 119–142; Sb. Math., 196:3 (2005), 423–445

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/msb1278
• https://doi.org/10.4213/sm1278
• http://mi.mathnet.ru/eng/msb/v196/i3/p119

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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, “Dva obschikh usloviya nedopustimosti spektralnogo sinteza dlya invariantnykh podprostranstv golomorfnykh funktsii”, Vladikavk. matem. zhurn., 7:3 (2005), 71–78
2. 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
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