Topics in global real analytic geometry [electronic resource] / Francesca Acquistapace, Fabrizio Broglia, José F. Fernando.

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Topics in global real analytic geometry [electronic resource] / Francesca Acquistapace, Fabrizio Broglia, José F. Fernando.

9783030966669 (electronic bk.)
3030966666 (electronic bk.)
3030966658
9783030966652

Cham, Switzerland : Springer, 2022.

English

1 online resource.

10.1007/978-3-030-96666-9 doi

QA551

516.3

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.

Includes bibliographical references and index.

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Online resource; title from PDF title page (Library Ideas, viewed June 16, 2022).

Springer monographs in mathematics.

Print version: 9783030966652

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