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Mat. Sb., 2005, Volume 196, Number 6, Pages 43–70 (Mi msb1364)  

This article is cited in 8 scientific papers (total in 8 papers)

Limit sets for the discrete spectrum of complex Jacobi matrices

L. B. Golinskii, I. E. Egorova

B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine

Abstract: The discrete spectrum of complex Jacobi matrices that are compact perturbations of the discrete Laplacian is studied. The precise stabilization rate (in the sense of order) of the matrix elements ensuring the finiteness of the discrete spectrum is found. An example of a Jacobi matrix with discrete spectrum having a unique limit point is constructed. These results are discrete analogues of Pavlov's well-known results on Schrödinger operators with complex potential on a half-axis.

DOI: https://doi.org/10.4213/sm1364

Full text: PDF file (419 kB)
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English version:
Sbornik: Mathematics, 2005, 196:6, 817–844

Bibliographic databases:

UDC: 517.5
MSC: 47B36, 47A10
Received: 02.02.2004

Citation: L. B. Golinskii, I. E. Egorova, “Limit sets for the discrete spectrum of complex Jacobi matrices”, Mat. Sb., 196:6 (2005), 43–70; Sb. Math., 196:6 (2005), 817–844

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. Arlinskii Yu., Tsekanovskii E., “Non-self-adjoint Jacobi matrices with a rank-one imaginary part”, J. Funct. Anal., 241:2 (2006), 383–438  crossref  mathscinet  isi
    2. L. Golinskii, M. Kudryavtsev, “On the discrete spectrum of complex banded matrices”, Zhurn. matem. fiz., anal., geom., 2:4 (2006), 396–423  mathnet  mathscinet  zmath  elib
    3. Golinskii L., Kupin S., “Lieb-Thirring bounds for complex Jacobi matrices”, Lett. Math. Phys., 82:1 (2007), 79–90  crossref  mathscinet  zmath  adsnasa  isi
    4. Hansmann M., Katriel G., “Inequalities for the Eigenvalues of Non-Selfadjoint Jacobi Operators”, Complex Anal Oper Theory, 5:1 (2011), 197–218  crossref  mathscinet  zmath  isi
    5. Golinskii L., Kupin S., “A Blaschke-type condition for analytic functions on finitely connected domains. Applications to complex perturbations of a finite-band selfadjoint operator”, J Math Anal Appl, 389:2 (2012), 705–712  crossref  mathscinet  zmath  isi
    6. Frank R.L., Simon B., “Eigenvalue Bounds For Schrodinger Operators With Complex Potentials. II”, J. Spectr. Theory, 7:3 (2017), 633–658  crossref  mathscinet  zmath  isi
    7. Judge E., Naboko S., Wood I., “Embedded Eigenvalues For Perturbed Periodic Jacobi Operators Using a Geometric Approach”, J. Differ. Equ. Appl., 24:8 (2018), 1247–1272  crossref  mathscinet  zmath  isi  scopus
    8. Swiderski G., “Spectral Properties of Some Complex Jacobi Matrices”, Integr. Equ. Oper. Theory, 92:2 (2020)  crossref  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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