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Teoreticheskaya i Matematicheskaya Fizika, 2019, Volume 200, Number 3, Pages 494–506
DOI: https://doi.org/10.4213/tmf9648
(Mi tmf9648)
 

This article is cited in 5 scientific papers (total in 5 papers)

Local perturbation of the discrete Schrödinger operator and a generalized Chebyshev oscillator

V. V. Borzova, E. V. Damaskinskyb

a St. Petersburg State University of Telecommunications, St. Petersburg, Russia
b Institute of Defence Technical Engineering, St. Petersburg, Russia
Full-text PDF (433 kB) Citations (5)
References:
Abstract: We discuss the conditions under which a special linear transformation of the classical Chebyshev polynomials $($of the second kind$)$ generate a class of polynomials related to "local perturbations" of the coefficients of a discrete Schrödinger equation. These polynomials are called generalized Chebyshev polynomials. We answer this question for the simplest class of "local perturbations" and describe a generalized Chebyshev oscillator corresponding to generalized Chebyshev polynomials.
Keywords: Jacobi matrix, orthogonal polynomials, classical Chebyshev polynomial, generalized Chebyshev polynomial, generalized Chebyshev oscillator.
Received: 29.10.2018
Revised: 29.04.2019
English version:
Theoretical and Mathematical Physics, 2019, Volume 200, Issue 3, Pages 1348–1359
DOI: https://doi.org/10.1134/S0040577919090083
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. V. Borzov, E. V. Damaskinsky, “Local perturbation of the discrete Schrödinger operator and a generalized Chebyshev oscillator”, TMF, 200:3 (2019), 494–506; Theoret. and Math. Phys., 200:3 (2019), 1348–1359
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/tmf9648
  • https://doi.org/10.4213/tmf9648
  • https://www.mathnet.ru/eng/tmf/v200/i3/p494
  • This publication is cited in the following 5 articles:
    1. V. V. Borzov, E. V. Damaskinsky, “Calculation of the Mandel Parameter for an Oscillator-Like System Generated by Generalized Chebyshev Polynomials”, J Math Sci, 277:4 (2023), 523  crossref
    2. V. V. Borzov, E. V. Damaskinsky, “Realization by a Differential Operator of the Annihilation Operator for Generalized Chebyshev Oscillator”, J Math Sci, 264:3 (2022), 252  crossref
    3. V. V. Borzov, E. V. Damaskinskii, “Vychislenie parametra Mandelya dlya ostsillyatoropodobnoi sistemy, porozhdaemoi obobschennymi polinomami Chebysheva”, Matematicheskie voprosy teorii rasprostraneniya voln. 50, Posvyaschaetsya devyanostoletiyu Vasiliya Mikhailovicha BABIChA, Zap. nauchn. sem. POMI, 493, POMI, SPb., 2020, 73–87  mathnet
    4. V. V. Borzov, E. V. Damaskinskii, “Realizatsiya operatora unichtozheniya obobschennogo ostsillyatora Chebysheva differentsialnym operatorom”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 27, Zap. nauchn. sem. POMI, 494, POMI, SPb., 2020, 75–102  mathnet
    5. Borzov V.V., Damaskinsky V E., “Some Identities For Generalized Chebyshev Polynomials”, Proceedings of the International Conference Days on Diffraction (Dd) 2019, eds. Motygin O., Kiselev A., Goray L., Fedotov A., Kazakov A., Kirpichnikova A., IEEE, 2019, 17–21  crossref  isi
    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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    Abstract page:283
    Full-text PDF :68
    References:71
    First page:7
     
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