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Teoreticheskaya i Matematicheskaya Fizika, 2011, Volume 169, Number 2, Pages 229–240
DOI: https://doi.org/10.4213/tmf6724 (Mi tmf6724) 		 
This article is cited in 4 scientific papers (total in 4 papers)

N-symmetric Chebyshev polynomials in a composite model of a generalized oscillator

V. V. Borzova, E. V. Damaskinskyb

a Saint-Petersburg State University of Telecommunications, St. Petersburg, Russia
b Saint Petersburg Military Engineering-Technical University, St. Petersburg, Russia
Full-text PDF (428 kB) Citations (4)
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DOI: https://doi.org/10.4213/tmf6724
Abstract: We continue to study a composite model of a generalized oscillator generated by an N-periodic Jacobi matrix. The foundation of the model is a system of orthogonal polynomials connected to this matrix for N=3,4,5. We show that such polynomials do not exist for N⩾6.
Keywords: generalized oscillator, Chebyshev polynomial, classical moment problem.
Received: 19.11.2011
English version:
Theoretical and Mathematical Physics, 2011, Volume 169, Issue 2, Pages 1561–1572
DOI: https://doi.org/10.1007/s11232-011-0133-8
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. V. Borzov, E. V. Damaskinsky, “N-symmetric Chebyshev polynomials in a composite model of a generalized oscillator”, TMF, 169:2 (2011), 229–240; Theoret. and Math. Phys., 169:2 (2011), 1561–1572
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/tmf6724
  • https://doi.org/10.4213/tmf6724
  • https://www.mathnet.ru/eng/tmf/v169/i2/p229
    • This publication is cited in the following 4 articles:
    1. V. V. Borzov, E. V. Damaskinsky, “Local perturbation of the discrete Schrödinger operator and a generalized Chebyshev oscillator”, Theoret. and Math. Phys., 200:3 (2019), 1348–1359  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. V. V. Borzov, E. V. Damaskinsky, “The discrete spectrum of Jacobi matrix related to recurrence relations with periodic coefficients”, J. Math. Sci. (N. Y.), 213:5 (2016), 694–705  mathnet  crossref  mathscinet
    3. V. V. Borzov, E. V. Damaskinsky, “Differential equations for the elementary 3-symmetric Chebyshev polynomials”, J. Math. Sci. (N. Y.), 192:1 (2013), 37–49  mathnet  crossref  mathscinet
    4. V.V. Borzov, E.V. Damaskinsky, 2012 Proceedings of the International Conference Days on Diffraction, 2012, 42  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:88
    First page:13
     
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