RATIONAL MOMENT PROBLEMS FOR COMPACT-SETS

The following ''rational'' moment problem is discussed. Given distinct real numbers lambda(1), lambda(2),..., lambda(p) (the ''poles'' of the problem), real numbers c(0) and c(j)((i)) (j = 1, 2, 3,...; i = 1, 2,..., p), and a non-empty compact subset K of (- infinity, + infinity), find necessary and sufficient conditions that there exist a non-negative Borel measure mu, supported on K, such that c(0) = integral(K) d mu(t) and c(j)((i)) = integral(K)(t - lambda(i))(-j) d mu(t) for j = 1, 2, 3,... and i = 1, 2,..., p. (C) 1994 Academic Press, Inc.