Topics in Global Real Analytic Geometry
In the first two chapters we review the theory developped by Cartan, Whitney and Tognoli. Then Nullstellensatz is proved both for Stein algebras and for the algebra of real analytic functions on a C-analytic space. Here we find a relation between real Nullstellensatz and seventeenth Hilbert’s problem for positive semidefinite analytic functions. Namely, a positive answer to Hilbert’s problem impli...
In the first two chapters we review the theory developped by Cartan, Whitney and Tognoli. Then Nullstellensatz is proved both for Stein algebras and for the algebra of real analytic functions on a C-analytic space. Here we find a relation between real Nullstellensatz and seventeenth Hilbert’s problem for positive semidefinite analytic functions. Namely, a positive answer to Hilbert’s problem impli...