On the pythagoras numbers of real analytic set germs.
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 Py...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2005 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/49907 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/49907 |
| Access Level: | acceso abierto |
| Palavra-chave: | 512.7 Pythagoras number sum of squares M. Artin’s approximation. Geometria algebraica 1201.01 Geometría Algebraica |
| Resumo: | 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. |
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