Acquistapace, FrancescaBroglia, FabrizioFernando Galván, José Francisco2023-06-202023-06-2020091871-248710.1007/s11512-008-0082-0https://hdl.handle.net/20.500.14352/42161We 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.engjournal articlehttp://www.arkivformatematik.org/http://www.springerlink.com/restricted access512.7Real analytic setAnalytic functionMeromorphic functionPositivstellensatzSums of quaresPositive semidefinite function sums of quarespositive semidefinite functionGeometria algebraica1201.01 Geometría Algebraica