Realization by a differential operator of the annihilation operator for generalized Chebyshev oscillator

We study a generalized Chebyshev oscillator [1] associated with a point interaction for the discrete Schrödinger operator. Our goal is to find a realization of the annihilation operator for this oscillator by a differential operator. This realization can be used to obtain a differential equation for the corresponding generalized Chebyshev polynomials [2]. This report is a continuation of our work [1, 3].