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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Sur le 17ème problème de Hilbert pour les fonctions de Nash
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by Jacek Bochnak PDF
Proc. Amer. Math. Soc. 71 (1978), 183-188 Request permission


The purpose of this note is to give a more refined version of a theorem of Efroymson: If $U \subset {{\mathbf {R}}^n}$ is defined by polynomial inequalities of the form ${f_i} > 0,i = 1, \ldots ,p$, 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.
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 71 (1978), 183-188
  • MSC: Primary 32B05; Secondary 12D99
  • DOI:
  • MathSciNet review: 0486597