Algebra of polynomials bounded on a semi-algebraic set \([ f\leq r ]\) (Q2667222)

In the paper under review, the authors study the problem whether the algebra of polynomials in \(n\) real variables which are bounded on the closed semi-algebraic set \(\{x \in \mathbb{R}^n \ : \ f(x) \le r\}\) is generated by a finite set of monomials, where \(f\) is a polynomial in \(n\) real variables and \(r\) is a real number. In terms of Newton polyhedrons, they provide some sufficient and necessary conditions such that the considered algebra is generated by a finite set of monomials.