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 | 0747-7171 |
| 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 |
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