Topics in Global Real Analytic Geometry

Released on by Francesca Acquistapace
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  • Topics in Global Real Analytic Geometry Book Detail

  • Author : Francesca Acquistapace
  • Release Date : 2022-06-07
  • Publisher : Springer Nature
  • Genre : Mathematics
  • Pages : 285
  • ISBN 13 : 3030966666
  • File Size : 97,97 MB
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Topics in Global Real Analytic Geometry by Francesca Acquistapace PDF Summary

Book Description: 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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