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＜電子ブック＞
Topics in Global Real Analytic Geometry / by Francesca Acquistapace, Fabrizio Broglia, José F. Fernando
(Springer Monographs in Mathematics. ISSN:21969922)

版	1st ed. 2022.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2022
本文言語	英語
大きさ	XVII, 273 p. 3 illus : online resource
著者標目	*Acquistapace, Francesca author Broglia, Fabrizio author Fernando, José F author SpringerLink (Online service)
件　名	LCSH:Algebraic geometry FREE:Algebraic Geometry
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-030-96666-9

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