# A new rational and continuous solution for Hilbert's 17th problem.

Extracta Mathematicae (1992)

• Volume: 7, Issue: 1, page 59-64
• ISSN: 0213-8743

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## Abstract

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In this note it is presented a new rational and continuous solution for Hilbert's 17th problem, which asks if an everywhere positive polynomial can be expressed as a sum of squares of rational functions. This solution (Theorem 1) improves the results in [2] in the sense that our parametrized solution is continuous and depends in a rational way on the coefficients of the problem (what is not the case in the solution presented in [2]). Moreover our method simplifies the proof and it is easy to generalize to other situations: for example in [4 or 5] we improve the results obtained in [7] giving more general rational and continuous solutions for several instances of Positivstellensatz (Theorem 2).

## How to cite

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Delzell, Charles N., González-Vega, Laureano, and Lombardi, Henri. "A new rational and continuous solution for Hilbert's 17th problem.." Extracta Mathematicae 7.1 (1992): 59-64. <http://eudml.org/doc/39966>.

@article{Delzell1992,
abstract = {In this note it is presented a new rational and continuous solution for Hilbert's 17th problem, which asks if an everywhere positive polynomial can be expressed as a sum of squares of rational functions. This solution (Theorem 1) improves the results in [2] in the sense that our parametrized solution is continuous and depends in a rational way on the coefficients of the problem (what is not the case in the solution presented in [2]). Moreover our method simplifies the proof and it is easy to generalize to other situations: for example in [4 or 5] we improve the results obtained in [7] giving more general rational and continuous solutions for several instances of Positivstellensatz (Theorem 2).},
author = {Delzell, Charles N., González-Vega, Laureano, Lombardi, Henri},
journal = {Extracta Mathematicae},
keywords = {Problema 17 de Hilbert; Campos ordenados; Análisis constructivo},
language = {eng},
number = {1},
pages = {59-64},
title = {A new rational and continuous solution for Hilbert's 17th problem.},
url = {http://eudml.org/doc/39966},
volume = {7},
year = {1992},
}

TY - JOUR
AU - Delzell, Charles N.
AU - González-Vega, Laureano
AU - Lombardi, Henri
TI - A new rational and continuous solution for Hilbert's 17th problem.
JO - Extracta Mathematicae
PY - 1992
VL - 7
IS - 1
SP - 59
EP - 64
AB - In this note it is presented a new rational and continuous solution for Hilbert's 17th problem, which asks if an everywhere positive polynomial can be expressed as a sum of squares of rational functions. This solution (Theorem 1) improves the results in [2] in the sense that our parametrized solution is continuous and depends in a rational way on the coefficients of the problem (what is not the case in the solution presented in [2]). Moreover our method simplifies the proof and it is easy to generalize to other situations: for example in [4 or 5] we improve the results obtained in [7] giving more general rational and continuous solutions for several instances of Positivstellensatz (Theorem 2).
LA - eng
KW - Problema 17 de Hilbert; Campos ordenados; Análisis constructivo
UR - http://eudml.org/doc/39966
ER -

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