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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
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
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
Linking options:
https://www.mathnet.ru/eng/tmf9648https://doi.org/10.4213/tmf9648 https://www.mathnet.ru/eng/tmf/v200/i3/p494
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Abstract page: | 235 | Full-text PDF : | 43 | References: | 58 | First page: | 6 |
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