Abstract:
We study subspaces invariant under differentiation in spaces of analytic functions in convex domains of the complex plane. For arbitrary convex domains we get a criterion for analytic continuation of functions from arbitrary non-trivial closed invariant subspaces admitting spectral
synthesis.
Citation:
A. S. Krivosheev, “A criterion for analytic continuation of functions from invariant subspaces in convex domains of the complex plane”, Izv. Math., 68:1 (2004), 43–76
\Bibitem{Kri04}
\by A.~S.~Krivosheev
\paper A~criterion for analytic continuation of functions from invariant subspaces in convex domains of the complex plane
\jour Izv. Math.
\yr 2004
\vol 68
\issue 1
\pages 43--76
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\crossref{https://doi.org/10.1070/IM2004v068n01ABEH000466}
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Linking options:
https://www.mathnet.ru/eng/im466
https://doi.org/10.1070/IM2004v068n01ABEH000466
https://www.mathnet.ru/eng/im/v68/i1/p43
This publication is cited in the following 12 articles:
A. Krivosheev, A. Rafikov, S. V. Kislyakov, “Representation of analytic functions in bounded convex domains on the complex plane”, St. Petersburg Math. J., 34:5 (2023), 775
A. S. Krivosheev, O. A. Krivosheeva, “Invariant Spaces of Entire Functions”, Math. Notes, 109:3 (2021), 413–426
A. S. Krivosheev, O. A. Krivosheeva, “Invariant subspaces in unbounded domains”, Probl. anal. Issues Anal., 10(28):3 (2021), 91–107
V. B. Sherstyukov, “Asymptotic properties of entire functions with given laws of distribution of zeros”, J. Math. Sci. (N. Y.), 257:2 (2021), 246–272
G. G. Braichev, V. B. Sherstyukov, “Sharp bounds for asymptotic characteristics of growth of entire functions with zeros on given sets”, J. Math. Sci., 250:3 (2020), 419–453
O. A. Krivosheyeva, A. S. Krivosheyev, “A representation of functions from an invariant subspace with almost real spectrum”, St. Petersburg Math. J., 29:4 (2018), 603–641
S. G. Merzlyakov, S. V. Popenov, “Interpolation by series of exponentials in H(D) with real nodes”, Ufa Math. J., 7:1 (2015), 46–57
A.V. Abanin, R. Ishimura, Le Hai Khoi, “Extension of solutions of convolution equations in spaces of holomorphic functions with polynomial growth in convex domains”, Bulletin des Sciences Mathématiques, 2011
A. S. Krivosheev, “Criterion of analytic continuability of functions in principal invariant subspaces on convex domains in Cn”, St. Petersburg Math. J., 22:4 (2011), 615–655
A. S. Krivosheev, “Invariantnye podprostranstva v vypuklykh oblastyakh iz Cn”, Ufimsk. matem. zhurn., 1:2 (2009), 53–74
A. S. Krivosheev, “Invariantnye podprostranstva v vypuklykh oblastyakh iz Cn”, Ufimsk. matem. zhurn., 1:3 (2009), 65–86
A. S. Krivosheev, “Continuation of functions from principal invariant subspaces”, Doklady Mathematics, 74:2 (2006), 728–730
Citation in format AMSBIB
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