, Volume 15, Issue 2, pp 297–307 | Cite as

Positivstellensätze for differentiable functions

  • Andreas Fischer


We present a canonical proof of both the strict and weak Positivstellensatz for rings of differentiable and smooth functions. Our construction is explicit, 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.


Positivstellensatz Differentiable and smooth function Definably complete structure Banach space 

Mathematics Subject Classification (2000)

Primary 03C64 14P10 Secondary 46E25 26E40 


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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Fields InstituteTorontoCanada
  2. 2.Gymnasium St. Ursula DorstenDorstenGermany

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