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.
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
This publication is cited in the following 5 articles:
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
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
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
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
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