Real Algebraic and Analytic Geometry Preprint Server

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Submission: 2009, April 30.

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 those rings of smooth functions which are definable in a polynomially bounded structure.

Mathematics Subject Classification (2000): 03C64, 14P10; Secondary 13J30, 26E10.

Keywords and Phrases: Positivstellensatz, analytic and smooth function, polynomially bounded structure.

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