Comment on "On the dimensions of the oscillator algebras induced by orthogonal polynomials" [J. Math. Phys. 55, 093511 (2014)]
Abstract
In the interesting paper G. Honnouvo and K. Thirulogasanthar [J. Math. Phys. 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.
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