Real Algebraic and Analytic Geometry
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Submission: 2005, September 1.
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 as to get completely satisfactory results for analytic curves and normal analytic surfaces.
Mathematics Subject Classification (2000): 14P99, 11E25, 32B10.
Keywords and Phrases: Positivstellensatz, sum of squares, positive semidefinite analytic function, compact set, analytic curve, normal analytic surface.
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