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Mat. Sb., 2010, Volume 201, Number 11, Pages 41–76 (Mi msb7603)  

This article is cited in 4 scientific papers (total in 4 papers)

Spectral decomposition of model operators in de Branges spaces

G. M. Gubreeva, A. A. Tarasenkob

a Poltava National Technical University named after Yuri Kondratyuk
b Universidad Autónoma del Estado de Hidalgo

Abstract: The paper is devoted to studying a class of completely continuous nonselfadjoint operators in de Branges spaces of entire functions. Among other results, a class of unconditional bases of de Branges spaces consisting of values of their reproducing kernels is constructed. The operators that are studied are model operators in the class of completely continuous non-dissipative operators with two-dimensional imaginary parts.
Bibliography: 22 titles.

Keywords: de Branges spaces, nonselfadjoint operators, the Muckenhoupt condition, unconditional bases consisting of values of reproducing kernels.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm7603

Full text: PDF file (732 kB)
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English version:
Sbornik: Mathematics, 2010, 201:11, 1599–1634

Bibliographic databases:

UDC: 517.583+517.518
MSC: Primary 47B32; Secondary 30D15, 46E22, 47A10, 47A70
Received: 16.07.2009 and 24.06.2010

Citation: G. M. Gubreev, A. A. Tarasenko, “Spectral decomposition of model operators in de Branges spaces”, Mat. Sb., 201:11 (2010), 41–76; Sb. Math., 201:11 (2010), 1599–1634

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. D. Baranov, D. V. Yakubovich, “One-dimensional perturbations of unbounded selfadjoint operators with empty spectrum”, J. Math. Anal. Appl., 424:2 (2015), 1404–1424  crossref  mathscinet  zmath  isi  elib  scopus
    2. Belov Yu., Lyubarskii Yu., “On Summation of Nonharmonic Fourier Series”, Constr. Approx., 43:2 (2016), 291–309  crossref  mathscinet  zmath  isi  scopus
    3. Baranov A.D., Yakubovich D.V., “Completeness and spectral synthesis of nonselfadjoint one-dimensional perturbations of selfadjoint operators”, Adv. Math., 302 (2016), 740–798  crossref  mathscinet  zmath  isi  scopus
    4. A. D. Baranov, “Spectral theory of rank one perturbations of normal compact operators”, Algebra i analiz, 30:5 (2018), 1–56  mathnet
  • Математический сборник Sbornik: Mathematics (from 1967)
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