This paper is concerned with
the moment problems associated with a sequence of orthogonal polynominals defined
by a recurrence formula. The principle interest centers on the question of the
determinacy of the Stieltjes moment problem in the case where the corresponding
Hamburger moment problem is indeterminate. Necessary and sufficient conditions
expressed in terms of the recurrence formula are obtained for an indeterminate
Hamburger moment problem to be a determined Stieltjes moment problem.
Using this result, various criteria concerning the determinacy of the moment
problems are obtained. It is also shown that if an indeterminate Hamburger
moment problem has at least one solution whose spectrum is bounded below,
then there is an extremal solution ψ∗ such that every substantially different
solution has at least one spectral point smaller than the least spectral point of
ψ∗.
