Real Algebraic and Analytic Geometry

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130. Niels Schwartz:
About Schmüdgen's Theorem.


Submission: 2004, August 30.

Schmüdgen proved a Positivstellensatz about the representation of positive definite polynomials on a basic closed semialgebraic set using methods from functional analysis in connection with Stengle's Positivstellensatz. Later Wörmann gave a purely algebraic proof. The present note contains yet another proof that uses classical results by Kadison about the representation of partially ordered algebras and the Theorem of Krein-Milman.

Full text, 9p.: pdf 39k.

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