Impossibility of \(C^{\infty}\) variation or formal power series variation in solutions to Hilbert's 17th problem
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Publication:1881118
DOI10.1016/j.jalgebra.2003.10.032zbMath1092.14069OpenAlexW2128916519MaRDI QIDQ1881118
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
sums of squaresHilbert's 17th problemformal power seriesWeierstrass polynomialspositive semidefinite polynomials\(C^\infty\) functionsbasic closed semianalytic sets
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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