Chihara关于壳多项式和不定矩问题的一个问题
A question by Chihara about shell polynomials and indeterminate moment problems
摘要：
讨论了含参数0 \le p<1和0<q<1的广义Stieltjes-Wigert多项式.通过从Nevanlinna参数化中去除集中在D函数零点的N-极值解的零点处的质量，我们得到了由其矩唯一确定的离散测度μ^M。我们计算相应的正交多项式（P^M_n）的系数。正如Chihara所指出的，这些多项式是对应于某个链序列的最大参数序列的壳多项式。我们还找到了最小参数序列，以及相应的广义Stieltjes-Wigert多项式的参数序列，并计算相关的连分数的值。海曼、伊斯梅尔-张和胡贝尔在最近的论文中研究了μ^M的质点。在p=q的特殊情况下，最大参数序列为常数，μ^M和（P^M_n）的确定回答了Chihara在2001年提出的一个问题
英文摘要：
The generalized Stieltjes--Wigert polynomials depending on parameters 0\le p<1 and 0<q<1 are discussed. By removing the mass at zero of the N-extremal solution concentrated in the zeros of the D-function from the Nevanlinna parametrization, we obtain a discrete measure μ^M which is uniquely determined by its moments. We calculate the coefficients of the corresponding orthonormal polynomials (P^M_n). As noticed by Chihara, these polynomials are the shell polynomials corresponding to the maximal parameter sequence for a certain chain sequence. We also find the minimal parameter sequence, as well as the parameter sequence corresponding to the generalized Stieltjes--Wigert polynomials, and compute the value of related continued fractions. The mass points of μ^M have been studied in recent papers of Hayman, Ismail--Zhang and Huber. In the special case of p=q, the maximal parameter sequence is constant and the determination of μ^M and (P^M_n) gives an answer to a question posed by Chihara in 2001
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