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On a global analytic Positivstellensatz

Francesca Acquistapace Dipartimento di Matematica, Università degli Studi di Pisa Fabrizio Broglia Dipartimento di Matematica, Università degli Studi di Pisa José F. Fernando Departamento de Álgebra, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid

TBD mathscidoc:1701.333141

Arkiv for Matematik, 47, (1), 13-39, 2007.2
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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@inproceedings{francesca2007on,
  title={On a global analytic Positivstellensatz},
  author={Francesca Acquistapace, Fabrizio Broglia, and José F. Fernando},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203624172618950},
  booktitle={Arkiv for Matematik},
  volume={47},
  number={1},
  pages={13-39},
  year={2007},
}
Francesca Acquistapace, Fabrizio Broglia, and José F. Fernando. On a global analytic Positivstellensatz. 2007. Vol. 47. In Arkiv for Matematik. pp.13-39. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203624172618950.
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