28 citations · 90 across the 20 of their papers we have counts for
20 papers
Calculating the Mandel parameter for an oscillator-like system generated by generalized Chebyshev polynomials
V. V. Borzov, E. V. Damaskinsky
In this paper, we calculate the Mandel parameter for an oscillator-like system generated by generalized Chebyshev polynomials \cite{01}, \cite{02}, \cite{03}. The sign of the…
Realization by a differential operator of the annihilation operator for generalized Chebyshev oscillator
V. V. Borzov, E. V. Damaskinsky
We study a generalized Chebyshev oscillator [1] associated with a point interaction for the discrete Schrödinger equation. Our goal is to find a realization of the annihilation ope…
On differential operators for bivariate Chebyshev polynomials
E. V. Damaskinsky, M. A Sokolov
We construct the differential operators for which bivariate Chebyshev polynomials of the first kind, associated with simple Lie algebras and , are eigenfunctions.
The generating function of bivariate Chebyshev polynomials associated with the Lie algebra
E. V. Damaskinsky, M. A. Sokolov
The generating function of the second kind bivariate Chebyshev polynomials associated with the simple Lie algebra is constructed by the method proposed in \cite{DKS} and \cit…
On the spectrum of discrete Schrödinger equation with one-dimensional perturbation
V. V. Borzov, E. V. Damaskinsky
We consider the spectrum of the discrete Schrödinger equation with one-dimensional perturbation. We obtain the explicit form of scattering matrix and find the exact condition of ab…
Invariance of the generalized oscillator under linear transformation of the related system of orthogonal polynomials
V. V. Borzov, E. V. Damaskinsky
We consider two families of polynomials $\mathbb{P}=\polP$ and $\mathbb{Q}=\polQ$\footnote{Here and below we consider only monic polynomials.} orthogonal on the real line with resp…