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On a global analytic Positivstellensatz.

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2009

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Springer Verlag
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We consider several modified versions of the Positivstellensatz for global analytic functions that involve infinite sums of squares and/or positive semidefinite analytic functions. We obtain a general local-global criterion which localizes the obstruction to have such a global result. This criterion allows us to get completely satisfactory results for analytic curves, normal analytic surfaces and real coherent analytic sets whose connected components are all compact.

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