Continuous functions on the plane regular after one blowing-up

详细信息    查看全文

• 作者：Goulwen Fichou ; Jean-Philippe Monnier ; Ronan Quarez
• 关键词：Regular function ; Regulous function ; Rational function ; Real algebraic variety ; Sum of squares
• 刊名：Mathematische Zeitschrift
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：285
• 期：1-2
• 页码：287-323
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-1823
• 卷排序：285

文摘

We study rational functions admitting a continuous extension to the real affine space. First of all, we focus on the regularity of such functions exhibiting some nice properties of their partial derivatives. Afterwards, since these functions correspond to rational functions which become regular after some blowings-up, we work on the plane where it suffices to blow-up points and then we can count the number of stages of blowings-up necessary. In the latest parts of the paper, we investigate the ring of rational continuous functions on the plane regular after one stage of blowings-up. In particular, we prove a Positivstellensatz without denominator in this ring.