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    3. Topics in Global Real Analytic Geometry

    Topics in Global Real Analytic Geometry

    Posted By: hill0
    Date: 12 Jun 2022 06:05:13
    Topics in Global Real Analytic Geometry

    Topics in Global Real Analytic Geometry
    English | 2022 | ISBN: 3030966658 | 290 Pages | PDF EPUB | 14 MB

    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.

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