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

Charles N. Delzell; Laureano González-Vega; Henri Lombardi

Extracta Mathematicae (1992)

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

## Access Full Article

top## Abstract

top## How to cite

topDelzell, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.