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Thirulogasanthar","submitted_at":"2015-09-03T22:29:47Z","abstract_excerpt":"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. 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Honnouvo, K. Thirulogasanthar","submitted_at":"2015-09-03T22:29:47Z","abstract_excerpt":"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. 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