Criterion of analytic continuability of functions in principal invariant subspaces on convex domains in $\mathbb {C}^{n}$
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A. S. Krivosheev
Translated by: the author - St. Petersburg Math. J. 22 (2011), 615-655
- DOI: https://doi.org/10.1090/S1061-0022-2011-01160-4
- Published electronically: May 3, 2011
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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.References
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Bibliographic 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
- Received by editor(s): April 1, 2009
- Published electronically: May 3, 2011
- © Copyright 2011 American Mathematical Society
- Journal: St. Petersburg Math. J. 22 (2011), 615-655
- MSC (2010): Primary 46E10, 47B38, 32D15, 32W50
- DOI: https://doi.org/10.1090/S1061-0022-2011-01160-4
- MathSciNet review: 2768963