Zeros of Sobolev orthogonal polynomials following from coherent pairs

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摘要

Let {Snλ} denote the monic orthogonal polynomial sequence with respect to the Sobolev inner product〈f,g〉S=∫−∞∞fgdψ0+λ∫−∞∞f′g′dψ1,where {dψ0,dψ1} is a so-called coherent pair and λ>0. Then Snλ has n different, real zeros. The position of these zeros with respect to the zeros of other orthogonal polynomials (in particular Laguerre and Jacobi polynomials) is investigated. Coherent pairs are found where the zeros of Sn−1λ separate the zeros of Snλ.

论文关键词:42C05,33C45,26C10,Orthogonal polynomials,Coherent pairs,Zeros,Gauss quadrature

论文评审过程:Received 10 October 2000, Available online 27 November 2001.

论文官网地址:https://doi.org/10.1016/S0377-0427(01)00421-6