Zeros of orthogonal Laurent polynomials and solutions of strong Stieltjes moment problems

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摘要

The strong Stieltjes moment problem for a bisequence {cn}n=−∞∞ consists of finding positive measures μ with support in [0,∞) such that ∫0∞tndμ(t)=cnfor n=0,±1,±2,…. Orthogonal Laurent polynomials associated with the problem play a central role in the study of solutions. When the problem is indeterminate, the odd and even sequences of orthogonal Laurent polynomials suitably normalized converge in C∖{0} to distinct holomorphic functions. The zeros of each of these functions constitute (together with the origin) the support of two solutions μ(∞) and μ(0). We discuss how odd and even subsequences of zeros of the orthogonal Laurent polynomials converge to the support points of μ(∞) and μ(0).

论文关键词:Strong moment problems,Orthogonal Laurent polynomials,Positive T-continued fractions,Natural solutions

论文评审过程:Received 20 August 2009, Available online 25 June 2010.

论文官网地址:https://doi.org/10.1016/j.cam.2010.06.015

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