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Topics in global real analy...

Topics in global real analytic geometry

Acquistapace, Francesca

Springer 2022

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 DenjoyCarleman functions. The book is addressed to researchers and Ph.D students interested in complex analysis and real analytic geometry

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monografia Rebiun31118409 https://catalogo.rebiun.org/rebiun/record/Rebiun31118409 m o d cr un|---aucuu 220614s2022 sz ob 001 0 eng d 1328135660 9783030966669 electronic bk.) 3030966666 electronic bk.) 3030966658 9783030966652 10.1007/978-3-030-96666-9 doi UPNA0555799 UR0541929 UAM 991008179241504211 UPVA 998152296103706 UCAR 991008309887004213 CUNEF 991000507353908131 CBUC 991010724376706709 CBUC 991012945253106708 YDX eng YDX GW5XE EBLCP MAT012010 bisacsh Acquistapace, Francesca Topics in global real analytic geometry Francesca Acquistapace, Fabrizio Broglia, José F. Fernando Cham, Switzerland Springer 2022 Cham, Switzerland Cham, Switzerland Springer 1 online resource 1 online resource Springer monographs in mathematics Includes bibliographical references and index 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 DenjoyCarleman functions. The book is addressed to researchers and Ph.D students interested in complex analysis and real analytic geometry Geometry, Analytic Electronic books Broglia, Fabrizio 1948-) Fernando, José F. Original 3030966658 9783030966652 (OCoLC)1293060156 Springer monographs in mathematics

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monografia Rebiun31118409 https://catalogo.rebiun.org/rebiun/record/Rebiun31118409 m o d cr un|---aucuu 220614s2022 sz ob 001 0 eng d 1328135660 9783030966669 electronic bk.) 3030966666 electronic bk.) 3030966658 9783030966652 10.1007/978-3-030-96666-9 doi UPNA0555799 UR0541929 UAM 991008179241504211 UPVA 998152296103706 UCAR 991008309887004213 CUNEF 991000507353908131 CBUC 991010724376706709 CBUC 991012945253106708 YDX eng YDX GW5XE EBLCP MAT012010 bisacsh Acquistapace, Francesca Topics in global real analytic geometry Francesca Acquistapace, Fabrizio Broglia, José F. Fernando Cham, Switzerland Springer 2022 Cham, Switzerland Cham, Switzerland Springer 1 online resource 1 online resource Springer monographs in mathematics Includes bibliographical references and index 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 DenjoyCarleman functions. The book is addressed to researchers and Ph.D students interested in complex analysis and real analytic geometry Geometry, Analytic Electronic books Broglia, Fabrizio 1948-) Fernando, José F. Original 3030966658 9783030966652 (OCoLC)1293060156 Springer monographs in mathematics