Real Algebraic and Analytic Geometry
Submission: 2005, September 1.
An algebra of analytic functions on a complex analytic space can be endowed with a topology in such a way that closed ideals behave specially well. For instance, a closed ideal $\alpha$ admits a primary decomposition, $\alpha =\bigcap _i \alpha _i$. In fact, under some restrictions on the ideals $\alpha _i$, the Hilbert Nullstellensatz holds for the ideal $\alpha$. In this work we look for similar conditions in the real case.
Mathematics Subject Classification (2000): 14P99, 11E25, 32B10.
Keywords and Phrases: Nullstellensatz, sum of squares, positive semidefinite analytic function, compact set, analytic curve, normal analytic surface.
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