Geodesic
Realization by a differential operator of the annihilation operator for generalized Chebyshev oscillator
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 27, Tome 494 (2020), pp. 75-102

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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]. 
@article{ZNSL_2020_494_a4,
     author = {V. V. Borzov and E. V. Damaskinskiy},
     title = {Realization by a differential operator of the annihilation operator for generalized {Chebyshev} oscillator},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {75--102},
     publisher = {mathdoc},
     volume = {494},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_494_a4/}
}
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V. V. Borzov; E. V. Damaskinskiy. Realization by a differential operator of the annihilation operator for generalized Chebyshev oscillator. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 27, Tome 494 (2020), pp. 75-102. http://geodesic.mathdoc.fr/item/ZNSL_2020_494_a4/