On dimensions of oscillator algebras

In a recent article (Honnouvo, Thirulogasanthar, arXiv:1305.2509) the authors discussed the question: under which conditions the oscillator algebra connected with orthogonal polynomials on real line is finite-dimensional. In the article, only the case when polynomials are orthogonal with respect to a symmetric measure on the real axis was considered. Here we point some omission and extend the results of the work to the case when measure is not symmetric. In conclusion we give some remarks about the oscillator algebras associated with two-dimensional polynomials.