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TMF, 2019, Volume 200, Number 3, Pages 494–506 (Mi tmf9648)  

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

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.

DOI: https://doi.org/10.4213/tmf9648

Full text: PDF file (433 kB)
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English version:
Theoretical and Mathematical Physics, 2019, 200:3, 1348–1359

Bibliographic databases:

Received: 29.10.2018
Revised: 29.04.2019

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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  • http://mi.mathnet.ru/eng/tmf9648
  • https://doi.org/10.4213/tmf9648
  • http://mi.mathnet.ru/eng/tmf/v200/i3/p494

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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. 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
    2. 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
    3. 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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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