Continous, piecewise-polynomial functions which solve Hilbert's 17th problem.

DOI10.1515/crll.1993.440.157zbMath0774.12003OpenAlexW4248562887MaRDI QIDQ4695255

Charles N. Delzell

Publication date: 17 June 1993

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://www.digizeitschriften.de/dms/resolveppn/?PPN=GDZPPN002210754

zbMATH Keywords

real spectrumHilbert's 17th problemreal closed fieldStellensätzepiecewise-polynomial functionsalmost \(f\)-ringscontinuous PWP functionsSIPD functionsStengle's Nichtnegativstellensatzsup-inf-polynomially definable functions

Mathematics Subject Classification ID

Real algebraic sets (14P05) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15)

Related Items (8)

Impossibility of \(C^{\infty}\) variation or formal power series variation in solutions to Hilbert's 17th problem ⋮ Uniform denominators in Hilbert's seventeenth problem ⋮ Positivity certificates and polynomial optimization on non-compact semialgebraic sets ⋮ Extending piecewise polynomial functions in two variables ⋮ Continuity properties for flat families of polynomials. I: Continuous parametrizations ⋮ Dependence on parameters in analogues of hilberts seventeenth problem ⋮ Positivity and Optimization: Beyond Polynomials ⋮ A real Nullstellensatz and Positivstellensatz for the semipolynomials over an ordered field

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