On the Pythagoras numbers of real analytic set germs

2005Bulletin de la Société mathématique de FranceMathematics被引 4开放获取

摘要

We show that (i) the Pythagoras number of a real analytic set germ is the supremum of the Pythagoras numbers of the curve germs it contains, and (ii) every real analytic curve germ is contained in a real analytic surface germ with the same Pythagoras number (or Pythagoras number 2 if the curve is Pythagorean). This gives new examples and counterexamples concerning sums of squares and positive semidefinite analytic function germs.

引用本文（GB/T 7714）

José F. Fernando, Jesús M. Ruíz. On the Pythagoras numbers of real analytic set germs[J]. Bulletin de la Société mathématique de France, 2005.

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DOI：https://doi.org/10.24033/bsmf.2490

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