A strict Positivstellensatz for rings of definable analytic functions
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- Proc. Amer. Math. Soc. 141 (2013), 1415-1422 Request permission
Abstract:
Consider an expansion of the real field in which every unary definable continuous function can be ultimately majorized by a definable analytic function. We prove the strict Positivstellensatz for analytic functions which are definable in such structures. The methods also work for a large class of quasianalytic subrings of the ring of those smooth functions that are definable in a polynomially bounded structure.References
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Additional Information
- Andreas Fischer
- Affiliation: Gymnasium St. Ursula, Ursulastrasse 8-10, Dorsten, Germany
- Address at time of publication: Comenius Gymnasium Datteln, Südring 150, 45711 Datteln, Germany
- Email: el.fischerandreas@live.de
- Received by editor(s): April 21, 2009
- Received by editor(s) in revised form: May 1, 2010, February 7, 2011, and July 12, 2011
- Published electronically: December 31, 2012
- Additional Notes: The author is a postdoctoral fellow of the Thematic Program on o-minimal Structures and Real Analytic Geometry at the Fields Institute
- Communicated by: Julia Knight
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 1415-1422
- MSC (2010): Primary 03C64, 14P10; Secondary 13J30, 26E10
- DOI: https://doi.org/10.1090/S0002-9939-2012-11361-9
- MathSciNet review: 3008888