Real Algebraic and Analytic Geometry
Submission: 2009, April 11.
We present a canonical proof of both the strict and weak Positivstellensatz for rings of differentiable and smooth functions. The construction preserves definability in expansions of the real field, and it works in definably complete expansions of real closed fields as well as for real-valued functions on Banach spaces.
Keywords and Phrases: Positivstellensatz, differentiable and smooth function, definably complete structure, Banach space.
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