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Funktsional. Anal. i Prilozhen., 2012, Volume 46, Issue 4, Pages 14–30 (Mi faa3086)  

This article is cited in 10 scientific papers (total in 10 papers)

A Criterion for the Fundamental Principle to Hold for Invariant Subspaces on Bounded Convex Domains in the Complex Plane

O. A. Krivosheevaa, A. S. Krivosheevb

a Bashkir State University, Ufa
b Institute of Mathematics with Computing Centre of Ural Branch of the USSR Academy of Sciences

Abstract: Let $D$ be a bounded convex domain of the complex plane. We study the problem of whether the fundamental principle holds for analytic function spaces on $D$ invariant with respect to the differentiation operator and admitting spectral synthesis. Earlier this problem was solved under a restriction on the multiplicities of the eigenvalues of the differentiation operator. In the present paper, we lift this restriction. Thus, we present a complete solution of the fundamental principle problem for arbitrary nontrivial closed invariant subspaces admitting spectral synthesis on arbitrary bounded convex domains.

Keywords: analytic function, convex domain, invariant subspace, fundamental principle

DOI: https://doi.org/10.4213/faa3086

Full text: PDF file (209 kB)
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English version:
Functional Analysis and Its Applications, 2012, 46:4, 249–261

Bibliographic databases:

UDC: 517.537.7
Received: 24.12.2010

Citation: 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”, Funktsional. Anal. i Prilozhen., 46:4 (2012), 14–30; Funct. Anal. Appl., 46:4 (2012), 249–261

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. Krivosheyev, O. A. Krivosheyeva, “A closedness of set of Dirichlet series sums”, Ufa Math. J., 5:3 (2013), 94–117  mathnet  crossref  elib
    2. 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
    3. 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
    4. 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
    5. 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
    6. 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
    7. O. A. Krivosheeva, “Basis in invariant subspace of analytical functions”, Ufa Math. J., 10:2 (2018), 58–77  mathnet  crossref  isi
    8. 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
    9. 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  isi
    10. A. S. Krivosheev, O. A. Krivosheeva, “Invariant subspaces in half-plane”, Ufa Math. J., 12:3 (2020), 30–43  mathnet  crossref
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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