Journal article
The role of Gröbner bases in the study of extremal truncated moment problems
Journal of mathematical analysis and applications, Vol.567(1), 131113
10/05/2026
DOI: 10.1016/j.jmaa.2026.131113
Abstract
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∈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.
Details
- Title: Subtitle
- The role of Gröbner bases in the study of extremal truncated moment problems
- Creators
- Raúl E. Curto - University of IowaMarc R. Moore - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Journal of mathematical analysis and applications, Vol.567(1), 131113
- DOI
- 10.1016/j.jmaa.2026.131113
- ISSN
- 0022-247X
- eISSN
- 1096-0813
- Publisher
- Elsevier
- Grant note
- U.S. NSF: DMS-2247167
The authors are deeply indebted to the Referee for a careful reading of the paper and for several edits and suggestions that helped improve the paper's content and presentation. The first-named author was partially supported by U.S. NSF grant DMS-2247167. Several examples in this paper were obtained using calculations with the software tool Mathematica [19] .
- Language
- English
- Date published
- 10/05/2026
- Academic Unit
- Mathematics
- Record Identifier
- 9985242768402771
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