关于“正交多项式诱导的振荡器代数的维数”的评论[J. Math. Phys. { \bf 55}，093511（2014）]
Comment on "On the dimensions of the oscillator algebras induced by orthogonal polynomials" [J. Math. Phys. {\bf 55}, 093511 (2014)]
摘要：
在有趣的论文G. Honnouvo和K. Thirulogasanthar [J. Math. Phys. { \bf 55}，093511（2014）]中，作者得到了与实数线上的正交多项式连接的振子代数是有限维的充要条件（并且在这种情况下代数的维数总是等于4）。在引用的文章中，只考虑了多项式关于实轴上的对称测度正交的情况。不幸的是，本文的充分条件是不完整的。本文澄清了该文献中相应定理的充分部分，并将结果推广到测度不对称的情形。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
