V. V. Borzov, E. V. Damaskinsky, “Local perturbation of the discrete Schrödinger operator and a generalized Chebyshev oscillator”, TMF, 2019, Volume 200, Number 3,Pages <nobr>494

This article is cited in 5 papers

Local perturbation of the discrete Schrödinger operator and a generalized Chebyshev oscillator

V. V. Borzov^a, E. V. Damaskinsky^b

^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

DOI: 10.4213/tmf9648