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arXiv · 1910.05251

The moment problem on curves with bumps

David Kimsey·Mihai Putinar
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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.

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David Kimsey, Mihai Putinar. 2020-07-24. The moment problem on curves with bumps. https://arxiv.org/abs/1910.05251

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