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TitleCurves testing boundedness of polynomials on subsets of the real plane
Author(s) Maria Michalska
TypeArticle in Journal
AbstractAbstract Let S ⊂ R 2 be a semialgebraic set. We exhibit a family of semialgebraic plane curves Γ_c , c ⩾ 0 , such that a polynomial f ∈ R [ X , Y ] is bounded on S if and only if it is bounded on a finite number of curves from this family. This number depends on S and degf. More precisely, each Γ_c is a sum of at most l continuous semialgebraic curves Γ_i^c , each parametrized by a Puiseux polynomial, where the number l and the family of curves Γ_i c depend on the set S only. To this aim we describe the algebras of bounded polynomials on tentacles of the set S which determine the algebra of polynomials bounded on S.
KeywordsBounded polynomials, Semialgebraic sets, Puiseux series
URL http://www.sciencedirect.com/science/article/pii/S0747717113000606
JournalJournal of Symbolic Computation
Pages107 - 124
Translation No
Refereed No