N-symmetric Chebyshev polynomials in a composite model of a generalized oscillator

摘要

We continue to study a composite model of a generalized oscillator generated by an N-periodic Jacobi matrix. The foundation of the model is a system of orthogonal polynomials connected to this matrix for N = 3, 4, 5. We show that such polynomials do not exist for N ≥ 6.