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Mat. Zametki, 2009, Volume 86, Issue 6, Pages 845–858 (Mi mz6624)  

This article is cited in 3 scientific papers (total in 3 papers)

On Compact Perturbations of the Limit-Periodic Jacobi Operator

V. A. Kalyagina, A. A. Kononovab

a State University – Higher School of Economics, Nizhny Novgorod Branch
b Nizhny Novgorod State Technical University

Abstract: We consider a bounded Jacobi operator acting in the space $l^2(\mathbb N)$. We supplement the spectral measure of this operator by a set of finitely many discrete masses (on the real axis outside the convex hull of the support of the operator's spectral measure). In the present paper, we study whether the obtained perturbation of the original operator is compact. For limit-periodic Jacobi operators, we obtain a necessary and sufficient condition on the location of the masses for the perturbation to be compact.

Keywords: compact perturbations, Jacobi operator, spectral measure, discrete masses, the space $\ell^2(\mathbb N)$, finite-zone operator, harmonic function

DOI: https://doi.org/10.4213/mzm6624

Full text: PDF file (521 kB)
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English version:
Mathematical Notes, 2009, 86:6, 789–800

Bibliographic databases:

UDC: 517.984
Received: 05.12.2008

Citation: V. A. Kalyagin, A. A. Kononova, “On Compact Perturbations of the Limit-Periodic Jacobi Operator”, Mat. Zametki, 86:6 (2009), 845–858; Math. Notes, 86:6 (2009), 789–800

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. A. Kononova, “On compact perturbations of finite-zone Jacobi operators”, J. Math. Sci. (N. Y.), 165:4 (2010), 473–482  mathnet  crossref  elib  elib
    2. A. Kh. Khanmamedov, “The inverse scattering problem for a discrete Sturm-Liouville equation on the line”, Sb. Math., 202:7 (2011), 1071–1083  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. A. I. Aptekarev, V. I. Buslaev, A. Martínez-Finkelshtein, S. P. Suetin, “Padé approximants, continued fractions, and orthogonal polynomials”, Russian Math. Surveys, 66:6 (2011), 1049–1131  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Математические заметки Mathematical Notes
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