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Topics in global real analytic geometry

Acquistapace, Francesca.

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Topics in global real analytic geometry

Record Type:	Electronic resources : Monograph/item
Title/Author:	Topics in global real analytic geometry/ by Francesca Acquistapace, Fabrizio Broglia, Jose F. Fernando.
Author:	Acquistapace, Francesca.
other author:	Broglia, Fabrizio.
Published:	Cham :Springer International Publishing : : 2022.,
Description:	xvii, 273 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Geometry, Analytic. -
Online resource:	https://doi.org/10.1007/978-3-030-96666-9
ISBN:	9783030966669

Topics in global real analytic geometry
Acquistapace, Francesca.

Topics in global real analytic geometry[electronic resource] /by Francesca Acquistapace, Fabrizio Broglia, Jose F. Fernando. - Cham :Springer International Publishing :2022. - xvii, 273 p. :ill., digital ;24 cm. - Springer monographs in mathematics,2196-9922. - Springer monographs in mathematics..

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.

ISBN: 9783030966669

Standard No.: 10.1007/978-3-030-96666-9doiSubjects--Topical Terms:

516181
Geometry, Analytic.

LC Class. No.: QA551 / .A36 2022

Dewey Class. No.: 516.3

Topics in global real analytic geometry
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490 1 $a Springer monographs in mathematics, $x 2196-9922
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.
650 0 $a Geometry, Analytic. $3 516181
650 1 4 $a Algebraic Geometry. $3 893861
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