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 ...
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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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Add this copy of Topics in Global Real Analytic Geometry to cart. $131.11, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2023 by Springer Nature Switzerland AG.
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New. Print on demand Contains: Illustrations, black & white. Springer Monographs in Mathematics . XVII, 273 p. 3 illus. Intended for professional and scholarly audience.
Add this copy of Topics in Global Real Analytic Geometry to cart. $131.11, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Springer Nature Switzerland AG.
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New. Print on demand Contains: Illustrations, black & white. Springer Monographs in Mathematics . XVII, 273 p. 3 illus. Intended for professional and scholarly audience.
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New. Contains: Illustrations, black & white. Springer Monographs in Mathematics . XVII, 273 p. 3 illus. Intended for professional and scholarly audience.
Add this copy of Topics in Global Real Analytic Geometry (Springer to cart. $162.64, new condition, Sold by Just one more Chapter rated 3.0 out of 5 stars, ships from Miramar, FL, UNITED STATES, published 2023 by Springer.
