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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)
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DOI: https://doi.org/10.4213/tmf9648
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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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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