Geodesic
Invariant subspaces of analytic functions. Analytic continuation
Izvestiya. Mathematics , Tome 7 (1973) no. 4, pp. 933-947.

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Let $G$ be a region in the complex plane; let $H$ be the space of functions analytic in $G$ with the topology of uniform convergence on compacta of $G$; let $W$ be a nontrivial invariant (with respect to differentiation) subspace in $H$ which admits a spectral synthesis. We investigate conditions for which all functions of $W$ can be analytically continued to a larger region $G'\supset G$. 
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I. F. Krasichkov-Ternovskii. Invariant subspaces of analytic functions. Analytic continuation. Izvestiya. Mathematics , Tome 7 (1973) no. 4, pp. 933-947. http://geodesic.mathdoc.fr/item/IM2_1973_7_4_a8/

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