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• W2022049738 abstract "We consider orthogonal polynomials with respect to a linear differential operator $$mathcal{L}^{(M)}=sum_{k=0}^{M}rho_{k}(z)frac{d^k}{dz^k}, $$ where ${rho_k}_{k=0}^{M}$ are complex polynomials such that $deg[rho_k]leq k, 0leq k leq M$, with equality for at least one index. We analyze the uniqueness and zero location of these polynomials. An interesting phenomenon occurring in this kind of orthogonality is the existence of operators for which the associated sequence of orthogonal polynomials reduces to a finite set. For a given operator, we find a classification of the measures for which it is possible to guarantee the existence of an infinite sequence of orthogonal polynomials, in terms of a linear system of difference equations with varying coefficients. Also, for the case of a first-order differential operator, we locate the zeros and establish the strong asymptotic behavior of these polynomials." @default.
• W2022049738 created "2016-06-24" @default.
• W2022049738 creator A5027797107 @default.
• W2022049738 date "2013-03-01" @default.
• W2022049738 modified "2023-09-27" @default.
• W2022049738 title "On orthogonal polynomials with respect to a class of differential operators" @default.
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• W2022049738 doi "https://doi.org/10.1016/j.amc.2013.01.069" @default.
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