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arXiv · 1509.01293

On the dimensions of oscillator-like algebras induced by orthogonal polynomials: non-symmetric case

G. Honnouvo·K. Thirulogasanthar
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Abstract

There is a generalized oscillator-like algebra associated with every class of orthogonal polynomials $\{\Psi_n(x)\}_{n=0}^{\infty}$, on the real line, satisfying a four term non-symmetric recurrence relation $x\Psi_n(x)=b_n\Psi_{n+1}(x)+a_n\Psi_n(x)+b_{n-1}\Psi_{n-1}(x),~\Psi_0(x)=1,~b_{-1}=0$. This note presents necessary and sufficient conditions on $a_n$ and $b_n$ for such algebras to be of finite dimension. As examples, we discuss the dimensions of oscillator-like algebras associated with Laguerre and Jacobi polynomials.

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G. Honnouvo, K. Thirulogasanthar. 2015-09-03. On the dimensions of oscillator-like algebras induced by orthogonal polynomials: non-symmetric case. https://doi.org/10.1016/s0034-4877(17)30021-6

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