The Multidimensional Moment Problem with Complexity Constraint
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.
Cite
@article{arxiv.1504.03626,
title = {The Multidimensional Moment Problem with Complexity Constraint},
author = {Johan Karlsson and Anders Lindquist and Axel Ringh},
journal= {arXiv preprint arXiv:1504.03626},
year = {2016}
}
Comments
25 pages. Revision: minor corrections