Leseprobe
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Topics in Global Real Analytic Geometry
Francesca Acquistapace, José F. Fernando, Fabrizio Broglia, et al.
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Springer International Publishing 
Naturwissenschaften, Medizin, Informatik, Technik / Arithmetik, Algebra
Beschreibung
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 implies a solution for the real Nullstellensatz more similar to the one for real polinomials. A chapter is devoted to the state of the art on this problem that is far from a complete answer.
In the last chapter we deal with inequalities. We describe a class of semianalytic sets defined by countably many global real analytic functions that is stable under topological properties and under proper holomorphic maps between Stein spaces, that is, verifies a direct image theorem. A smaller class admits also a decomposition into irreducible components as it happens for semialgebraic sets. Duringthe redaction some proofs have been simplified with respect to the original ones.
Kundenbewertungen
Strict Positivstellensatz, Global semianalytic sets, Nullstellensatz for Stein spaces and real analytic spaces, Divisors in C-analytic Sets, Infinite sums of squares, Irreducible components., Pytagoras number, Real analytic spaces, Excellent rings, Complex analytic spaces, Pfister's forms and matrices, Artin-Schreier theory, C-semianalytic sets, Normalization, Amenable C-semianalytic sets and irreducible components