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The moment problem on curves with bumps

Lookup NU author(s): Dr David KimseyORCiD, Emeritus Professor Mihai Putinar

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This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).

Abstract

© 2020, The Author(s). 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.

Publication metadata

Author(s): Kimsey DP, Putinar M

Publication type: Article

Publication status: Published

Journal: Mathematische Zeitschrift

Year: 2021

Volume: 298

Pages: 935-942

Print publication date: 01/08/2021

Online publication date: 27/10/2020

Acceptance date: 14/09/2020

Date deposited: 11/11/2020

ISSN (print): 0025-5874

ISSN (electronic): 1432-1823

Publisher: Springer Science and Business Media Deutschland GmbH

URL: https://doi.org/10.1007/s00209-020-02633-2

DOI: 10.1007/s00209-020-02633-2

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