Abstract
On the space, A of Laurent polynomials we consider a linear functional L which is positive definite on (0,∞) and is defined in terms of a given bisequence, { c k } k=−∞ ∞. For each ω>0, we define a sequence { N n ( z, ω)} n=0 ∞ of rational functions in terms of two sequences of orthogonal Laurent polynomials, { Q n ( z)} n=0 ∞ and { Q ̂ n(z)} n=0 ∞ , which span A in the order {1, z −1, z, z −2, z 2,…} and {1, z, z −1, z 2, z −2,…}, respectively. It is shown that the numerators and denominators of each N n ( z, ω) are linear combinations of the canonical numerators and denominators of a modified PC-fraction. Consequently, { N 2 n ( z, ω)} n=0 ∞ and { N 2 n+1 ( z, ω)} n=0 ∞ converge uniformly on compact subsets of C –{0} to analytic functions and hence lead to additional solutions to the strong Stieltjes moment problem.
Published Version
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