Real Algebraic and Analytic Geometry

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171. Francesca Acquistapace, Fabrizio Broglia, Josť F. Fernando:
On a Global Analytic Positivstellensatz.

e-mail: , ,

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.

Full text, 36p.: pdf 309k.

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