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Sur le 17ème problème de Hilbert pour les fonctions de Nash

Part of the Lecture Notes in Mathematics book series (LNM,volume 694)

Abstract

The purpose of this note is to give a more refined version of a theorem of Efroymson : If U ⊂ Rn is defined by polynomial inequalities of the form fi>0, i=1, ..., p, and if g is a positive definite Nash function on U, then g is a finite sum of squares of Nash meromorphe functions on U.

AMS 1970 subject classification

  • Primary 12D15
  • 14E99
  • 32C05
  • Key words and phrases
  • 17th Hilbert problem
  • Nash functions
  • Tarski principle
  • semi-algebraic sets
  • real closed field

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Bibliographie

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© 1978 Springer-Verlag

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Bochnak, J. (1978). Sur le 17ème problème de Hilbert pour les fonctions de Nash. In: Lelong, P., Skoda, H. (eds) Séminaire Pierre Lelong — Henri Skoda (Analyse) Année 1976/77. Lecture Notes in Mathematics, vol 694. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0063242

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  • DOI: https://doi.org/10.1007/BFb0063242

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09101-1

  • Online ISBN: 978-3-540-35552-6

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