Real Algebraic and Analytic Geometry |

About Schmüdgen's Theorem.

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homepage: http://www.fmi.uni-passau.de/lehrstuehle/schwartz/

Submission: 2004, August 30.

*Abstract:
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.:
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