The moment problem on curves with bumps
Functional Analysis
2020-07-28 v2 Algebraic Geometry
Abstract
The power moments of a positive measure on the real line or the circle are characterized by the non-negativity of an infinite matrix, Hankel, respectively Toeplitz, attached to the data. Except some fortunate configurations, in higher dimensions there are no non-negativity criteria for the power moments of a measure to be supported by a prescribed closed set. We combine two well studied fortunate situations, specifically a class of curves in two dimensions classified by Scheiderer and Plaumann, and compact, basic semi-algebraic sets, with the aim at enlarging the realm of geometric shapes on which the power moment problem is accessible and solvable by non-negativity certificates.
Cite
@article{arxiv.1910.05251,
title = {The moment problem on curves with bumps},
author = {David Kimsey and Mihai Putinar},
journal= {arXiv preprint arXiv:1910.05251},
year = {2020}
}