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arXiv · 1504.03626

The Multidimensional Moment Problem with Complexity Constraint

Johan Karlsson·Anders Lindquist·Axel Ringh
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Abstract

A long series of previous papers have been devoted to the (one-dimensional) moment problem with nonnegative rational measure. The rationality assumption is a complexity constraint motivated by applications where a parameterization of the solution set in terms of a bounded finite number of parameters is required. In this paper we provide a complete solution of the multidimensional moment problem with a complexity constraint also allowing for solutions that require a singular measure added to the rational, absolutely continuous one. Such solutions occur on the boundary of a certain convex cone of solutions. In this paper we provide complete parameterizations of all such solutions. We also provide errata for a previous paper in this journal coauthored by one of the authors of the present paper.

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Johan Karlsson, Anders Lindquist, Axel Ringh. 2015-04-14. The Multidimensional Moment Problem with Complexity Constraint. https://doi.org/10.1007/s00020-015-2248-z

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