Publication: On a global analytic Positivstellensatz.
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2009
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Springer Verlag
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Abstract
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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Acquistapace, F., Andradas, C. and Broglia, F., The strict Positivstellensatz for global analytic functions and the moment problem for semianalytic sets, Math.Ann. 316 (2000), 609–616.
Acquistapace, F., Broglia, F., Fernando, J. F. and Ruiz, J. M., On the Pythagoras numbers of real analytic surfaces, Ann. Sci. ´ Ecole Norm. Sup. 38 (2005), 751–772.
Acquistapace, F., Broglia, F., Fernando, J. F. and Ruiz, J. M., On the Pythagoras numbers of real analytic curves, Math. Z. 257 (2007), 13–21.
Acquistapace, F., Broglia, F., Fernando, J. F. and Ruiz, J. M., On the finiteness of Pythagoras numbers of real meromorphic functions, Preprint RAAG 185,2008. http://www.maths.manchester.ac.uk/raag/index.php?preprint=0185.
Acquistapace, F., Broglia, F. and Shiota, M., The finiteness property and Lojasiewicz inequality for global semianalytic sets, Adv. Geom. 5 (2005), 377–390.
Andradas, C. and Becker, E., A note on the real spectrum of analytic functions on an analytic manifold of dimension one, in Real Analytic and Algebraic Geometry (Trento, 1988), Lecture Notes in Math. 1420, pp. 1–21, Springer, Berlin–Heidelberg, 1990.