caa a22 4500 44586897X CHVBK 20180317145506.0 cr unu---uuuuu 170323e20110101xx s 000 0 eng 10.1007/s00605-010-0224-x doi (NATIONALLICENCE)springer-10.1007/s00605-010-0224-x Description of polygonal regions by polynomials of bounded degree [Elektronische Daten] [Gennadiy Averkov, Christian Bey] We show that every (possibly unbounded) convex polygon P in $${\mathbb{R}^2}$$ with m edges can be represented by inequalities p 1 ≥0, . . ., p n ≥ 0, where the p i's are products of at most k affine functions each vanishing on an edge of P and n=n(m, k) satisfies $${s(m, k) \leq n(m, k) \leq (1+\varepsilon_m) s(m, k)}$$ with s(m,k) ≔max {m/k, log2 m} and $${\varepsilon_m \rightarrow 0}$$ as $${m \rightarrow \infty}$$. This choice of n is asymptotically best possible. An analogous result on representing the interior of P in the form p 1 >0, . . ., p n > 0 is also given. For k ≤ m/log2 m these statements remain valid for representations with arbitrary polynomials of degree not exceeding k. Springer-Verlag, 2010 Gray code nationallicence Polygon nationallicence Polynomial nationallicence Semi-algebraic set nationallicence Theorem of Bröcker and Scheiderer nationallicence Averkov Gennadiy Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany aut Bey Christian Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany aut Monatshefte für Mathematik Springer Vienna 162/1(2011-01-01), 19-27 0026-9255 162:1<19 2011 162 605 https://doi.org/10.1007/s00605-010-0224-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00605-010-0224-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Averkov Gennadiy Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany aut NATIONALLICENCE 700 1- Bey Christian Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer Vienna 162/1(2011-01-01), 19-27 0026-9255 162:1<19 2011 162 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer