Abstract
We consider the families of polynomials P = { P n (x)} ∞ n=0 and Q = { Q n (x)} ∞ n=0 orthogonal on the real line with respect to the respective probability measures μ and ν. We assume that { Q n (x)} ∞ n=0 and {P n (x)} ∞ n=0 are connected by linear relations. In the case k = 2, we describe all pairs (P,Q) for which the algebras A P and A Q of generalized oscillators generated by { Qn(x)} ∞ n=0 and { Pn(x)} ∞ n=0 coincide. We construct generalized oscillators corresponding to pairs (P,Q) for arbitrary k ≥ 1.
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The research of E. V. Damaskinsky was supported by the Russian Foundation for Basic Research (Grant No. 15-01-03148).
Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 190, No. 2, pp. 267–276, February, 2017.
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Borzov, V.V., Damaskinsky, E.V. Invariance of the generalized oscillator under a linear transformation of the related system of orthogonal polynomials. Theor Math Phys 190, 228–236 (2017). https://doi.org/10.1134/S0040577917020052
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DOI: https://doi.org/10.1134/S0040577917020052