Comment on "On the dimensions of the oscillator algebras induced by orthogonal polynomials" [J. Math. Phys. {\bf 55}, 093511 (2014)]

TL;DR

This paper clarifies and extends previous results on the finite-dimensionality of oscillator algebras linked to orthogonal polynomials, including cases with non-symmetric measures, providing a more complete characterization.

Contribution

It completes the proof of the sufficient conditions for finite-dimensionality and extends the analysis to non-symmetric measures, broadening the applicability of the original results.

Findings

Confirmed the finite-dimensionality condition for symmetric measures

Extended the results to non-symmetric measures

Provided a complete proof of the sufficient conditions

Abstract

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 oscillator algebra connected with orthogonal polynomials on real line is finite-dimensional (and in this case the dimension of the algebra is always equal four). In the cited article, only the case when polynomials are orthogonal with respect to a symmetric measure on the real axis was considered. Unfortunately, the sufficient condition from this paper is incomplete. Here we clarify the sufficient part of the corresponding theorem from that paper and extend the results to the case when measure is not symmetric.