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Topics in Global Real Analytic Geometry

This book provides an exposition of the theory of analytic C-spaces developed by Cartan, Whitney and Tognoli and describes some central results in global real analytic geometry, such as Nullstellensatze and Positivstellensatze, including Forster's global Nullstellensatz for Stein algebras. It e...

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Bibliographic Details
Main Authors: Acquistapace, Francesca, Broglia, Fabrizio (Author), Fernando, José F. (Author)
Format: eBook
Language:English
Published: Cham Springer International Publishing 2022, 2022
Edition:1st ed. 2022
Series:Springer Monographs in Mathematics
Subjects:
Algebraic Geometry
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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520 |a This book provides an exposition of the theory of analytic C-spaces developed by Cartan, Whitney and Tognoli and describes some central results in global real analytic geometry, such as Nullstellensatze and Positivstellensatze, including Forster's global Nullstellensatz for Stein algebras. It emphasizes the central role of Hilbert's 17th Problem in this context, devoting a chapter to the state of the art on this difficult problem. The focus then turns to a class of semianalytic sets defined by countably many global real analytic functions, which is stable under topological operations and satisfies a direct image theorem. A smaller subclass admits a decomposition into irreducible components comparable to that for semialgebraic sets. The last chapter is dedicated to the extension of some of the preceding results to smooth functions and quasi-analytic Denjoy–Carleman functions. The book is addressed to researchers and Ph.D students interested in complex analysis and real analytic geometry 

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