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

The strong Stieltjes moment problem for a bisequence {cn}n=−∞∞ consists of finding positive measures μμ with support in [0,∞)[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}C∖{0} to distinct holomorphic functions. The zeros of each of these functions constitute (together with the origin) the support of two solutions μ(∞)μ(∞) and μ(0)μ(0). We discuss how odd and even subsequences of zeros of the orthogonal Laurent polynomials converge to the support points of μ(∞)μ(∞) and μ(0)μ(0).