Central Nullstellensätze in real analytic geometry (Q1184033)

In real algebraic geometry there exist several adaptations of Hilbert's Nullstellensatz, e.g. the real Nullstellensatz [cf. \textit{J. Bochnak}, \textit{M. Coste}, \textit{M.-F.Roy}, ``Géométrie algébrique réelle'' (1987; Zbl 0633.14016); corollaire 4.1.8] or the real central Nullstellensatz [cf. ibid., corollaire 7.6.5]. The latter result relates an ideal \(I\) in the coordinate ring of a real algebraic variety \(V\) to the ideal of functions vanishing on the zero set of \(I\) intersected with the set of central points of \(V\) (i.e., the euclidean closure of the regular points of \(V)\). In the present paper the notion of central points is introduced in the context of real analytic geometry. Descriptions of central points are given in terms of real spectra of rings of analytic functions and central Nullstellensätze are proved both for local and global real analytic geometry.