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ISBN: 3030966658 3030966666 Year: 2022 Publisher: Cham, Switzerland : Springer International Publishing,
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Geometry, Analytic. --- Geometry, Analytic --- Data processing. --- Analytical geometry --- Geometry, Algebraic --- Algebra --- Conic sections --- Graphic methods --- Geometria analítica --- Anàlisi geomètrica --- Geometria algebraica --- Coordenades --- Corbes
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ISBN: 9783030966669 9783030966652 9783030966676 9783030966683 Year: 2022 Publisher: Cham Springer International Publishing
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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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ISBN: 9783030966669 Year: 2022 Publisher: Cham Springer International Publishing :Imprint: Springer
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Geometria analítica --- Geometry, Analytic. --- Geometry, Analytic --- Data processing. --- Analytical geometry --- Geometry, Algebraic --- Algebra --- Conic sections --- Graphic methods
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