Geodesic
Local perturbation of the~discrete Schr\"odinger operator and a~generalized Chebyshev oscillator
Teoretičeskaâ i matematičeskaâ fizika, Tome 200 (2019) no. 3, pp. 494-506

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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.
Mots-clés : Jacobi matrix, orthogonal polynomials
Keywords: classical Chebyshev polynomial, generalized Chebyshev polynomial, generalized Chebyshev oscillator. 
@article{TMF_2019_200_3_a7,
     author = {V. V. Borzov and E. V. Damaskinsky},
     title = {Local perturbation of the~discrete {Schr\"odinger} operator and a~generalized {Chebyshev} oscillator},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {494--506},
     publisher = {mathdoc},
     volume = {200},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_200_3_a7/}
}
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V. V. Borzov; E. V. Damaskinsky. Local perturbation of the~discrete Schr\"odinger operator and a~generalized Chebyshev oscillator. Teoretičeskaâ i matematičeskaâ fizika, Tome 200 (2019) no. 3, pp. 494-506. http://geodesic.mathdoc.fr/item/TMF_2019_200_3_a7/