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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A strict Positivstellensatz for rings of definable analytic functions


Author: Andreas Fischer
Journal: Proc. Amer. Math. Soc. 141 (2013), 1415-1422
MSC (2010): Primary 03C64, 14P10; Secondary 13J30, 26E10
Published electronically: December 31, 2012
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11361-9
PII: S 0002-9939(2012)11361-9
Keywords: Positivstellensatz, analytic and smooth function, polynomially bounded structure
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
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.