Invariance of the generalized oscillator under a linear transformation of the related system of orthogonal polynomials |
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Authors: | V V Borzov E V Damaskinsky |
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Institution: | 1.St. Petersburg State University of Telecommunications,St. Petersburg,Russia;2.Military Institute (Engineering-Technical),Military Academy of Materiel and Technical Security,St. Petersburg,Russia |
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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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