Details:
Title  Curves testing boundedness of polynomials on subsets of the real plane  Author(s)  Maria Michalska  Type  Article in Journal  Abstract  Abstract 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.  Keywords  Bounded polynomials, Semialgebraic sets, Puiseux series  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717113000606 
Language  English  Journal  Journal of Symbolic Computation  Volume  56  Number  0  Pages  107  124  Year  2013  Edition  0  Translation 
No  Refereed 
No 
