Geodesic
Criterion of analytic continuability of functions in principal invariant subspaces on convex domains in~$\mathbb C^n$
Algebra i analiz, Tome 22 (2010) no. 4, pp. 137-197.

Voir la notice de l'article provenant de la source Math-Net.Ru

Subspaces invariant under differentiation are studied for spaces of functions analytic on domains of a many-dimensional complex space. For a wide class of domains (in particular, for arbitrary bounded convex domains), a criterion of analytic continuability is obtained for functions in arbitrary nontrivial closed principal invariant subspaces admitting spectral synthesis.
Keywords: analytic continuation, invariant subspace, plurisubharmonic function, convex domain. 
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A. S. Krivosheev. Criterion of analytic continuability of functions in principal invariant subspaces on convex domains in~$\mathbb C^n$. Algebra i analiz, Tome 22 (2010) no. 4, pp. 137-197. http://geodesic.mathdoc.fr/item/AA_2010_22_4_a4/

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