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Izv. RAN. Ser. Mat., 2004, Volume 68, Issue 2, Pages 71–136 (Mi izv476)  

This article is cited in 30 scientific papers (total in 30 papers)

A fundamental principle for invariant subspaces in convex domains

A. S. Krivosheev

Abstract: Under certain natural restrictions, we give a complete solution of the interpolation problem in spaces of entire functions of exponential type whose conjugate diagram is contained in a given convex domain. We also give a complete solution of the problem of finding a fundamental principle for arbitrary non-trivial closed subspaces of functions analytic in a convex domain that are invariant under differentiation and admit spectral synthesis.


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English version:
Izvestiya: Mathematics, 2004, 68:2, 291–353

Bibliographic databases:

UDC: 517.5
MSC: 30E05, 30D15, 30D20
Received: 31.10.2002

Citation: A. S. Krivosheev, “A fundamental principle for invariant subspaces in convex domains”, Izv. RAN. Ser. Mat., 68:2 (2004), 71–136; Izv. Math., 68:2 (2004), 291–353

Citation in format AMSBIB
\by A.~S.~Krivosheev
\paper A~fundamental principle for invariant subspaces in convex domains
\jour Izv. RAN. Ser. Mat.
\yr 2004
\vol 68
\issue 2
\pages 71--136
\jour Izv. Math.
\yr 2004
\vol 68
\issue 2
\pages 291--353

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    This publication is cited in the following articles:
    1. O. A. Krivosheeva, “Osobye tochki summy ryada eksonent na granitse oblasti skhodimosti”, Ufimsk. matem. zhurn., 1:4 (2009), 78–109  mathnet  zmath
    2. A. S. Krivosheev, “Pochti eksponentsialnyi bazis”, Ufimsk. matem. zhurn., 2:1 (2010), 87–96  mathnet  zmath  elib
    3. A. S. Krivosheev, “Bazisy “po otnositelno malym gruppam””, Ufimsk. matem. zhurn., 2:2 (2010), 67–89  mathnet  zmath  elib
    4. O. A. Krivosheeva, A. S. Krivosheev, “Fundamentalnyi printsip dlya invariantnykh podprostranstv”, Ufimsk. matem. zhurn., 2:4 (2010), 58–73  mathnet  zmath  elib
    5. O. A. Krivosheyeva, “Singular points of the sum of exponential monomials series on the boundary of convergence domain”, St. Petersburg Math. J., 23:2 (2012), 321–350  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    6. A. S. Krivosheev, “Pochti eksponentsialnaya posledovatelnost eksponentsialnykh mnogochlenov”, Ufimsk. matem. zhurn., 4:1 (2012), 88–106  mathnet
    7. O. A. Krivosheeva, A. S. Krivosheev, “A Criterion for the Fundamental Principle to Hold for Invariant Subspaces on Bounded Convex Domains in the Complex Plane”, Funct. Anal. Appl., 46:4 (2012), 249–261  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    8. A. S. Krivosheev, O. A. Krivosheeva, “A basis in an invariant subspace of analytic functions”, Sb. Math., 204:12 (2013), 1745–1796  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    9. A. S. Krivosheyev, O. A. Krivosheyeva, “A closedness of set of Dirichlet series sums”, Ufa Math. J., 5:3 (2013), 94–117  mathnet  crossref  elib
    10. O. A. Krivosheyeva, “Convergence domain for series of exponential polynomials”, Ufa Math. J., 5:4 (2013), 82–87  mathnet  crossref  elib
    11. Elias Zikkos, “Solutions of infinite order differential equations without the grouping phenomenon and a generalization of the Fabry–Pólya theorem”, Journal of Mathematical Analysis and Applications, 2014  crossref  mathscinet  scopus
    12. 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
    13. O. A. Krivosheeva, A. S. Krivosheev, “Singular points of the sum of a Dirichlet series on the convergence line”, Funct. Anal. Appl., 49:2 (2015), 122–134  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    14. V. B. Sherstyukov, “Distribution of the zeros of canonical products and weighted condensation index”, Sb. Math., 206:9 (2015), 1299–1339  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    15. A. S. Krivosheev, O. A. Krivosheyeva, “A basis in invariant subspace of entire functions”, St. Petersburg Math. J., 27:2 (2016), 273–316  mathnet  crossref  mathscinet  isi  elib
    16. A. S. Krivosheev, O. A. Krivosheeva, “Fundamental Principle and a Basis in Invariant Subspaces”, Math. Notes, 99:5 (2016), 685–696  mathnet  crossref  crossref  mathscinet  isi  elib
    17. A. I. Abdulnagimov, A. S. Krivosheyev, “Properly distributed subsets in complex plane”, St. Petersburg Math. J., 28:4 (2017), 433–464  mathnet  crossref  mathscinet  isi  elib
    18. A. I. Abdulnagimov, A. S. Krivoshyev, “Representation of analytic functions”, Ufa Math. J., 8:4 (2016), 3–23  mathnet  crossref  mathscinet  isi  elib
    19. 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
    20. O. A. Krivosheeva, “Invariant subspaces with zero density spectrum”, Ufa Math. J., 9:3 (2017), 100–108  mathnet  crossref  isi  elib
    21. O. A. Krivosheeva, “Basis in invariant subspace of analytical functions”, Ufa Math. J., 10:2 (2018), 58–77  mathnet  crossref  isi
    22. O. A. Krivosheeva, A. S. Krivosheev, “Singular points for the sum of a series of exponential monomials”, Probl. anal. Issues Anal., 7(25), spetsvypusk (2018), 72–87  mathnet  crossref  elib
    23. Ufa Math. J., 10:3 (2018), 142–148  mathnet  crossref  isi
    24. S. G. Merzlyakov, S. V. Popenov, “Interpolyatsiya summami ryadov eksponent s pokazatelyami, sguschayuschimisya v odnom napravlenii”, Kompleksnyi analiz. Matematicheskaya fizika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 162, VINITI RAN, M., 2019, 62–79  mathnet  mathscinet
    25. Merzlyakov S.G., Popenov S.V., “Interpolation By Sums of Series of Exponentials and Global Cauchy Problem For Convolution Operators”, Dokl. Math., 99:2 (2019), 149–151  crossref  isi
    26. O. A. Krivosheeva, A. S. Krivosheev, A. I. Rafikov, “Lower bounds for entire functions”, Ufa Math. J., 11:3 (2019), 44–60  mathnet  crossref  isi
    27. Krivosheev A., Krivosheeva O., “Representation of Analytic Functions By Series of Exponential Monomials in Convex Domains and Its Applications”, Lobachevskii J. Math., 40:9, SI (2019), 1330–1354  crossref  isi
    28. A. S. Krivosheev, O. A. Krivosheeva, “The distribution of singular points of the sum of a series of exponential monomials on the boundary of its domain of convergence”, Sb. Math., 211:1 (2020), 55–114  mathnet  crossref  crossref  mathscinet  isi
    29. A. S. Krivosheev, O. A. Krivosheeva, “Invariant subspaces in half-plane”, Ufa Math. J., 12:3 (2020), 30–43  mathnet  crossref  isi
    30. A. S. Krivosheev, O. A. Krivosheeva, “Invariant Spaces of Entire Functions”, Math. Notes, 109:3 (2021), 413–426  mathnet  crossref  crossref  mathscinet
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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