Acquistapace Francesca Acquistapace; Broglia Fabrizio Broglia; Fernando Jose F. Fernando Springer Nature B.V. (2022) Saatavuus: Hankintapalvelu Pehmeäkantinen kirja
A. Ismael F. Vaz (ed.); João Paulo Almeida (ed.); José Fernando Oliveira (ed.); Alberto Adrego Pinto (ed.) Springer (2018) Saatavuus: Tilaustuote Kovakantinen kirja
A. Ismael F. Vaz (ed.); João Paulo Almeida (ed.); José Fernando Oliveira (ed.); Alberto Adrego Pinto (ed.) Springer (2019) Saatavuus: Tilaustuote Pehmeäkantinen kirja
Carlos Chastre (ed.); José Neves (ed.); Diogo Ribeiro (ed.); Fernando F. S. Pinho (ed.); Hugo Biscaia (ed.); Maria G Neves Springer (2023) Saatavuus: Tilaustuote Kovakantinen kirja
Carlos Chastre (ed.); José Neves (ed.); Diogo Ribeiro (ed.); Fernando F. S. Pinho (ed.); Hugo Biscaia (ed.); Maria G Neves Springer (2024) Saatavuus: Tilaustuote Pehmeäkantinen kirja
Springer Sivumäärä: 273 sivua Asu: Kovakantinen kirja Julkaisuvuosi: 2022, 08.06.2022 (lisätietoa) Kieli: Englanti
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.