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This article is cited in 2 scientific papers (total in 2 papers)
Invariance of the generalized oscillator under a linear transformation of the related system of orthogonal polynomials
V. V. Borzova, E. V. Damaskinskyb a St. Petersburg State University of Telecommunications, St. Petersburg, Russia
b Military Institute (Engineering-Technical), Military Academy
of Materiel and Technical Security, St. Petersburg, Russia
Abstract:
We consider the families of polynomials $\mathbb P=\{P_n(x)\}_{n=0}^\infty$ and $\mathbb Q=\{Q_n(x)\}_{n=0}^\infty$ orthogonal on the real line with respect to the respective probability measures $\mu$ and $\nu$. We assume that $\{Q_n(x)\}_{n=0}^\infty$ and $\{P_n(x)\}_{n=0}^\infty$ are connected by linear relations. In the case $k=2$, we describe all pairs $(\mathbb P,\mathbb Q)$ for which the algebras $\mathfrak A_P$ and $\mathfrak A_Q$ of generalized oscillators generated by $\{Q_n(x)\}_{n=0}^\infty$ and $\{P_n(x)\}_{n=0}^\infty$ coincide. We construct generalized oscillators corresponding to pairs $(\mathbb P,\mathbb Q)$ for arbitrary $k\ge1$.
Keywords:
generalized oscillator, orthogonal polynomial.
Received: 09.12.2015 Revised: 10.04.2016
Citation:
V. V. Borzov, E. V. Damaskinsky, “Invariance of the generalized oscillator under a linear transformation of the related system of orthogonal polynomials”, TMF, 190:2 (2017), 267–276; Theoret. and Math. Phys., 190:2 (2017), 228–236
Linking options:
https://www.mathnet.ru/eng/tmf9118https://doi.org/10.4213/tmf9118 https://www.mathnet.ru/eng/tmf/v190/i2/p267
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Abstract page: | 317 | Full-text PDF : | 137 | References: | 35 | First page: | 17 |
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