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math.AG2023
Sums of squares representations on singular loci
Ngoc Hoang Anh Mai, Victor Magron
The problem of characterizing a real polynomial as a sum of squares of polynomials on a real algebraic variety dates back to the pioneering work of Hilbert in [Mathematisch…
math.AG2022★ 1 cited
Urysohn in action: separating semialgebraic sets by polynomials
Milan Korda, Jean-Bernard Lasserre, Alexey Lazarev +2
A classical result from topology called Uryshon's lemma asserts the existence of a continuous separator of two disjoint closed sets in a sufficiently regular topological space. In…
math.AG2020★ 2 cited
A sparse version of Reznick's Positivstellensatz
Ngoc Hoang Anh Mai, Victor Magron, Jean-Bernard Lasserre
If is a positive definite form, Reznick's Positivstellensatz [Mathematische Zeitschrift. 220 (1995), pp. 75--97] states that there exists such that ${\| x \|^{…