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- Title
Invariance of the generalized oscillator under a linear transformation of the related system of orthogonal polynomials.
- Authors
Borzov, V.; Damaskinsky, E.
- Abstract
We consider the families of polynomials P = { P ( x)} and Q = { Q ( x)} orthogonal on the real line with respect to the respective probability measures μ and ν. We assume that { Q ( x)} and { P ( x)} are connected by linear relations. In the case k = 2, we describe all pairs (P,Q) for which the algebras A and A of generalized oscillators generated by { Qn(x)} and { Pn(x)} coincide. We construct generalized oscillators corresponding to pairs (P,Q) for arbitrary k ≥ 1.
- Subjects
ORTHOGONAL polynomials; BOREL sets; VECTOR spaces; HANKEL functions; RECURSIVE sequences (Mathematics)
- Publication
Theoretical & Mathematical Physics, 2017, Vol 190, Issue 2, p228
- ISSN
0040-5779
- Publication type
Article
- DOI
10.1134/S0040577917020052