Impossibility of \(C^{\infty}\) variation or formal power series variation in solutions to Hilbert's 17th problem

DOI10.1016/j.jalgebra.2003.10.032zbMath1092.14069OpenAlexW2128916519MaRDI QIDQ1881118

Charles N. Delzell

Publication date: 4 October 2004

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2003.10.032

zbMATH Keywords

sums of squaresHilbert's 17th problemformal power seriesWeierstrass polynomialspositive semidefinite polynomials\(C^\infty\) functionsbasic closed semianalytic sets

Mathematics Subject Classification ID

Semialgebraic sets and related spaces (14P10) Ordered fields (12J15) Ordered rings (13J25) Real algebra (13J30)

Cites Work

• Continuous Pythagoras numbers for rational quadratic forms
• A continuous, constructive solution to Hilbert's \(17^{th}\) problem
• Some continuous Positivstellensätze
• Extremal positive semidefinite forms
• A real Nullstellensatz and Positivstellensatz for the semipolynomials over an ordered field
• Smooth parametrizations for several cases of the Positivstellensatz
• Uniform denominators in Hilbert's seventeenth problem
• Anneaux preordonnes
• Analytic Right-Inverses to Quadratic Forms over Number Fields
• Artin-Schreier theory for commutative regular rings
• An Artin-Lang property for germs of C∞ functions
• Continous, piecewise-polynomial functions which solve Hilbert's 17th problem.
• On the Representation of a Rational as a Sum of Four Squares By Means of Regular Functions
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