Geodesic
Spectral synthesis for the intersection of invariant subspaces of holomorphic functions
Sbornik. Mathematics, Tome 196 (2005) no. 3, pp. 423-445 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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B. N. Khabibullin. Spectral synthesis for the intersection of invariant subspaces of holomorphic functions. Sbornik. Mathematics, Tome 196 (2005) no. 3, pp. 423-445. http://geodesic.mathdoc.fr/item/SM_2005_196_3_a4/

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