  We study a generalized Chebyshev oscillator [1] associated with a point
interaction for the discrete Schr\"odinger equation. 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].
