We study a generalized Chebyshev oscillator associated with a point interaction for the discrete Schrödinger 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.
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To the memory of our friend V. D. Lyakhovsky
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 494, 2020, pp. 75–102.
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Borzov, V.V., Damaskinsky, E.V. Realization by a Differential Operator of the Annihilation Operator for Generalized Chebyshev Oscillator. J Math Sci 264, 252–270 (2022). https://doi.org/10.1007/s10958-022-05996-5
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DOI: https://doi.org/10.1007/s10958-022-05996-5