Springer Monographs in Mathematics- Topics in Global Real Analytic Geometry
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- Engels
- Hardcover
- 9783030966652
- 08 juni 2022
- 273 pagina's
Samenvatting
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.
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.
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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Inhoud
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- en
- Bindwijze
- Hardcover
- Oorspronkelijke releasedatum
- 08 juni 2022
- Aantal pagina's
- 273
Betrokkenen
- Hoofdauteur
- Francesca Acquistapace
- Tweede Auteur
- Fabrizio Broglia
- Hoofduitgeverij
- Springer Nature Switzerland AG
Overige kenmerken
- Editie
- 1st ed. 2022
- Product breedte
- 155 mm
- Product lengte
- 235 mm
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- Verpakking breedte
- 155 mm
- Verpakking hoogte
- 235 mm
- Verpakking lengte
- 235 mm
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- 606 g
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- EAN
- 9783030966652
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