The Role of Gröbner Bases in the Study of Extremal Truncated Moment Problems

Raúl E Curto; Marc R Moore

doi:10.48550/arxiv.2602.07386

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The Role of Gröbner Bases in the Study of Extremal Truncated Moment Problems

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The Role of Gröbner Bases in the Study of Extremal Truncated Moment Problems

Raúl E Curto and Marc R Moore

ArXiv.org

Cornell University

02/21/2026

DOI: 10.48550/arxiv.2602.07386

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

In a 2014 paper, R.E. Curto and S. Yoo proved that a moment matrix with specific harmonic polynomials as column relations admits a representing measure if and only if a condition at the level of moments holds. \ In this paper, we generalize the 2014 result to arbitrary moment matrices ( ), with column relations given by general harmonic polynomials. \ We accomplish this by proving that the Gröbner basis for the ideal generated by a finite variety associated with the moment matrix provides all the necessary column relations for the matrix as well as a suitable condition on the moments, which is equivalent to the existence of a representing measure.

Mathematics - Functional Analysis

Details

Title: Subtitle: The Role of Gröbner Bases in the Study of Extremal Truncated Moment Problems
Creators: Raúl E Curto - University of Iowa
Marc R Moore - University of Iowa
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2602.07386
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 02/21/2026
Academic Unit: Mathematics
Record Identifier: 9985139493002771

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