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Izv. RAN. Ser. Mat., 2004, Volume 68, Issue 1, Pages 43–78 (Mi izv466)  

This article is cited in 9 scientific papers (total in 9 papers)

A criterion for analytic continuation of functions from invariant subspaces in convex domains of the complex plane

A. S. Krivosheev


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.

DOI: https://doi.org/10.4213/im466

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English version:
Izvestiya: Mathematics, 2004, 68:1, 43–76

Bibliographic databases:

UDC: 517.5
MSC: 46E10, 30B40, 30D15, 44A10
Received: 03.09.2001

Citation: A. S. Krivosheev, “A criterion for analytic continuation of functions from invariant subspaces in convex domains of the complex plane”, Izv. RAN. Ser. Mat., 68:1 (2004), 43–78; Izv. Math., 68:1 (2004), 43–76

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. S. Krivosheev, “Continuation of functions from principal invariant subspaces”, Doklady Mathematics, 74:2 (2006), 728–730  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. S. Krivosheev, “Invariantnye podprostranstva v vypuklykh oblastyakh iz $\mathbb C^n$”, Ufimsk. matem. zhurn., 1:2 (2009), 53–74  mathnet  zmath  elib
    3. A. S. Krivosheev, “Invariantnye podprostranstva v vypuklykh oblastyakh iz $\mathbb C^n$”, Ufimsk. matem. zhurn., 1:3 (2009), 65–86  mathnet  zmath  elib
    4. A. S. Krivosheev, “Criterion of analytic continuability of functions in principal invariant subspaces on convex domains in $\mathbb C^n$”, St. Petersburg Math. J., 22:4 (2011), 615–655  mathnet  crossref  mathscinet  zmath  isi
    5. 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  crossref  mathscinet  isi  scopus
    6. 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  mathnet  crossref  isi  elib
    7. 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  mathnet  crossref  mathscinet  isi  elib
    8. G. G. Braichev, V. B. Sherstyukov, “Tochnye otsenki asimptoticheskikh kharakteristik rosta tselykh funktsii s nulyami na zadannykh mnozhestvakh”, Fundament. i prikl. matem., 22:1 (2018), 51–97  mathnet
    9. V. B. Sherstyukov, “Asimptoticheskie svoistva tselykh funktsii s zadannym zakonom raspredeleniya kornei”, Kompleksnyi analiz. Tselye funktsii i ikh primeneniya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 161, VINITI RAN, M., 2019, 104–129  mathnet
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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