RT Book, Whole
T1 Topics in Global Real Analytic Geometry
A1 Acquistapace, Francesca
A1 Broglia, Fabrizio
A1 Fernando Galván, José Francisco
AB 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. During the redaction some proofs have been simplified with respect to the original ones.
PB Springer
SN 978-3-030-96665-2
YR 2022
FD 2022
LK https://hdl.handle.net/20.500.14352/96131
UL https://hdl.handle.net/20.500.14352/96131
LA eng
NO Acquistapace, F, Fernando Galván, J. F. & Broglia, F. Topics in Global Real Analytic Geometry. Springer International Publishing, 2022. https://doi.org/10.1007/978-3-030-96666-9.
DS Docta Complutense
RD 20 abr 2025