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Criterion of analytic continuability of functions in principal invariant subspaces on convex domains in $ \mathbb{C}^{n}$


Author: A. S. Krivosheev
Translated by: the author
Original publication: Algebra i Analiz, tom 22 (2010), nomer 4.
Journal: St. Petersburg Math. J. 22 (2011), 615-655
MSC (2010): Primary 46E10, 47B38, 32D15, 32W50
Published electronically: May 3, 2011
MathSciNet review: 2768963
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Abstract | References | Similar Articles | Additional Information

Abstract: 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.


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Additional Information

A. S. Krivosheev
Affiliation: Mathematical Institute with Computer Center, Urals Scientific Center, Russian Academy of Sciences, Ul. Chernyshevskogo 112, Ufa 450077, Russia
Email: sasha@matem.anrb.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-2011-01160-4
Keywords: Analytic continuation, invariant subspace, plurisubharmonic function, convex domain
Received by editor(s): April 1, 2009
Published electronically: May 3, 2011
Article copyright: © Copyright 2011 American Mathematical Society