28 citations · 90 across the 20 of their papers we have counts for
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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…
Comment on "On the dimensions of the oscillator algebras induced by orthogonal polynomials" [J. Math. Phys. {\bf 55}, 093511 (2014)]
V. V. Borzov, E. V. Damaskinsky
In the interesting paper G. Honnouvo and K. Thirulogasanthar [J. Math. Phys. {\bf 55} , 093511 (2014)] the authors obtained the necessary and sufficient conditions under which the…
Orthogonal polynomials and deformed oscillators
V. V. Borzov, E. V. Damaskinsky
We discuss the construction of oscillator-like systems associated with orthogonal polynomials on the example of the Fibonacci oscillator. In addition, we consider the dimension of…
The discrete spectrum of Jacobi matrix related to recurrence relations with periodic coefficients
V. V. Borzov, E. V. Damaskinsky
In this note we investigate the discrete spectrum of Jacobi matrix corresponding to polynomials defined by recurrence relations with periodic coefficients. As examples we consider…
On calculation of generating functions of generalized Chebyshev polynomials in several variables
E. V. Damaskinsky, P. P. Kulish, M. A. Sokolov
We propose a new method of calculation of generating functions of Chebyshev polynomials in several variables associated with root systems of simple Lie algebras. We obtain the gene…