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


Author: Jacek Bochnak
Journal: Proc. Amer. Math. Soc. 71 (1978), 183-188
MSC: Primary 32B05; Secondary 12D99
DOI: https://doi.org/10.1090/S0002-9939-1978-0486597-2
MathSciNet review: 0486597
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Abstract | References | Similar Articles | Additional Information

Abstract: 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.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0486597-2
Keywords: 17th Hilbert problem, Nash functions, Tarski principle, semi-algebraic sets, real closed field
Article copyright: © Copyright 1978 American Mathematical Society

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