The Role of Gröbner Bases in the Study of Extremal Truncated Moment Problems
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914341276614656 |
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| author | Curto, Raúl E. Moore, Marc R. |
| author_facet | Curto, Raúl E. Moore, Marc R. |
| contents | In a 2014 paper, R.E. Curto and S. Yoo proved that a moment matrix $M(3)$ 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 $M(k)$ ($k \in \mathbb{Z}_{+}$), 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07386 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Role of Gröbner Bases in the Study of Extremal Truncated Moment Problems Curto, Raúl E. Moore, Marc R. Functional Analysis 47 In a 2014 paper, R.E. Curto and S. Yoo proved that a moment matrix $M(3)$ 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 $M(k)$ ($k \in \mathbb{Z}_{+}$), 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. |
| title | The Role of Gröbner Bases in the Study of Extremal Truncated Moment Problems |
| topic | Functional Analysis 47 |
| url | https://arxiv.org/abs/2602.07386 |