On the Pythagoras numbers of real analytic set germs

José F. Fernando; Jesús M. Ruiz

Bulletin de la Société Mathématique de France (2005)

  • Volume: 133, Issue: 3, page 349-362
  • ISSN: 0037-9484

Abstract

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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.

How to cite

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Fernando, José F., and Ruiz, Jesús M.. "On the Pythagoras numbers of real analytic set germs." Bulletin de la Société Mathématique de France 133.3 (2005): 349-362. <http://eudml.org/doc/272491>.

@article{Fernando2005,
abstract = {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.},
author = {Fernando, José F., Ruiz, Jesús M.},
journal = {Bulletin de la Société Mathématique de France},
keywords = {pythagoras number; sum of squares; m. Artin’s approximation},
language = {eng},
number = {3},
pages = {349-362},
publisher = {Société mathématique de France},
title = {On the Pythagoras numbers of real analytic set germs},
url = {http://eudml.org/doc/272491},
volume = {133},
year = {2005},
}

TY - JOUR
AU - Fernando, José F.
AU - Ruiz, Jesús M.
TI - On the Pythagoras numbers of real analytic set germs
JO - Bulletin de la Société Mathématique de France
PY - 2005
PB - Société mathématique de France
VL - 133
IS - 3
SP - 349
EP - 362
AB - 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.
LA - eng
KW - pythagoras number; sum of squares; m. Artin’s approximation
UR - http://eudml.org/doc/272491
ER -

References

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