English

The Multidimensional Moment Problem with Complexity Constraint

Optimization and Control 2016-04-07 v4 Functional Analysis

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.

Keywords

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

R2 v1 2026-06-22T09:15:56.547Z