Description: Topics in Global Real Analytic Geometry, Hardcover by Acquistapace, Francesca; Broglia, Fabrizio; Galvan, Jose F. Fernando, ISBN 3030966658, ISBN-13 9783030966652, Like New Used, Free shipping in the US 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.
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Book Title: Topics in Global Real Analytic Geometry
Number of Pages: Xvii, 273 Pages
Publication Name: Topics in Global Real Analytic Geometry
Language: English
Publisher: Springer International Publishing A&G
Publication Year: 2022
Subject: General, Geometry / Algebraic
Item Weight: 21.4 Oz
Type: Textbook
Author: Jose F. Fernando Galván, Francesca Acquistapace, Fabrizio Broglia
Subject Area: Mathematics
Item Length: 9.3 in
Item Width: 6.1 in
Series: Springer Monographs in Mathematics Ser.
Format: Hardcover
