Abstract
This paper is concerned with indeterminate classical Stieltjes moment problems (CSMPs) and indeterminate strong Stieltjes moment problems (SSMPs). We are particularly interested in what we call the natural solutions to each type of moment problem. Known results are summarized and we compare Stieltjes’ results on indeterminate CSMPs to analogous results for a special class of indeterminate SSMPs. For the indeterminate CSMP each natural solution is a step function whose points of increase have a limit point at ∞. Each natural solution to an indeterminate SSMP is a step function whose points of increase have limit points only at 0 and/or ∞. Every convex linear combination of the natural solutions to an indeterminate Stieltjes moment problem (classical and strong) is also a solution to that problem. It is shown that there exist indeterminate Stieltjes moment problems (both classical and strong) which have step function solutions which are not convex linear combinations of the natural solutions. Finally, it is shown how to construct new moment problems and their solutions from known moment problems and their solutions so that the moments of both problems are related by “shifts” and “flips.”
Published Version
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