A strict Positivstellensatz for rings of definable analytic functions

Fischer, Andreas

doi:10.1090/S0002-9939-2012-11361-9

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.

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