Topics in Global Real Analytic Geometry
Language: English
Published by Springer, Berlin|Springer International Publishing|Springer, 2023
- Softcover
- New
Seller: moluna, Greven, Germanymoluna
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Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 Nu.
Seller Inventory # 873621137
- Title
- Topics in Global Real Analytic Geometry
- Author
- Acquistapace, Francesca|Broglia, Fabrizio|Fernando, José F.
- Publisher
- Springer, Berlin|Springer International Publishing|Springer
- Publication year
- 2023
- Condition
- New
- Binding
- Kartoniert / Broschiert
- Language
- English
- ISBN 10
- 3030966682
- ISBN 13
- 9783030966683
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.
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