Vol. 27, No. 3, 1968

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On indeterminate Hamburger moment problems

Theodore Seio Chihara

Vol. 27 (1968), No. 3, 475–484

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.

Mathematical Subject Classification
Primary: 44.60
Received: 9 January 1967
Published: 1 December 1968
Theodore Seio Chihara