Unique solvability of an extended Hamburger moment problem

AbstractR-functions are rational functions with no poles in the extended complex plane outside a given set {a1,…, ap} of points on the real axis. Methods from the theory of orthogonal polynomials can be extended to R-functions. By this means the author solved an extended Hamburger moment problem: Given sequences of real numbers {cn(i): n = 1, 2,…}, i = 1,…, p, find conditions for a distribution function ψ to exist such that ∫−αα dψ(t) = 1, ∫−αα dψ(t)(t − ai)m = cm(i) m = 1, 2,…, i = 1,…, p. In this paper these methods are extended to treat conditions for the moment problem to have a unique solution. The results are related to the classical limit point-limit circle situation