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

The strong Stieltjes moment problem for a bisequence { c n } n = − ∞ ∞ consists of finding positive measures μ with support in [ 0 , ∞ ) such that ∫ 0 ∞ t n d μ ( t ) = c n for  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 ) .