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Mat. Sb., 2007, Volume 198, Number 6, Pages 107–138 (Mi msb3782)  

This article is cited in 7 scientific papers (total in 7 papers)

Trace formulae for a class of Jacobi operators

S. P. Suetin

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The class of Jacobi operators generated by unit Borel measures with support formed by finitely many intervals of the real line $\mathbb R$ and finitely many points in $\mathbb R$ lying outside the convex hull of these intervals is investigated. An asymptotic formula for the diagonal Green's function in this class is obtained as well as the trace formulae for sequences $a,b\in\ell^\infty(\mathbb N)$ corresponding to a fixed operator.
Bibliography: 39 titles.

DOI: https://doi.org/10.4213/sm3782

Full text: PDF file (759 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2007, 198:6, 857–885

Bibliographic databases:

UDC: 517.53+517.984.51+517.962
MSC: Primary 47B36, 30B70, 40A15; Secondary 41A21
Received: 18.10.2006

Citation: S. P. Suetin, “Trace formulae for a class of Jacobi operators”, Mat. Sb., 198:6 (2007), 107–138; Sb. Math., 198:6 (2007), 857–885

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. S. P. Suetin, “Strong asymptotics of zeros of polynomials orthogonal with respect to a complex-valued weight”, Russian Math. Surveys, 62:4 (2007), 823–825  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. V. A. Kalyagin, A. A. Kononova, “On Compact Perturbations of the Limit-Periodic Jacobi Operator”, Math. Notes, 86:6 (2009), 789–800  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. S. P. Suetin, “Strong asymptotics of polynomials orthogonal with respect to a complex weight”, Sb. Math., 200:1 (2009), 77–93  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. Peherstorfer F., “Orthogonal polynomials on several intervals: Accumulation points of recurrence coefficients and of zeros”, J. Approx. Theory, 163:7 (2011), 814–837  crossref  mathscinet  zmath  isi  elib  scopus
    5. 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
    6. 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
    7. I. E. Egorova, L. A. Pastur, “On asymptotic properties of polynomials orthogonal with respect to varying weights and related topics of spectral theory”, St. Petersburg Math. J., 25:2 (2014), 223–240  mathnet  crossref  mathscinet  zmath  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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