Título:
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On Hilbert 17th problem and real nullstellensatz for global analytic functions
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Autores:
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Ruiz Sancho, Jesús María
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Tipo de documento:
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texto impreso
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Editorial:
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Springer, 1985
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Dimensiones:
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application/pdf
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Nota general:
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info:eu-repo/semantics/restrictedAccess
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Idiomas:
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Geometria algebraica
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Materia = Ciencias: Matemáticas: Teoría de conjuntos
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Tipo = Artículo
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Resumen:
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The author proves a Nullstellensatz for the ring of real analytic functions on a compact analytic manifold. The main results are the following. Theorem 1: Let X be a compact irreducible analytic set of a real analytic manifold M and f:X?R a nonnegative analytic function. Then f is a sum of squares of meromorphic functions. Theorem 2: Let I be a finitely generated ideal of O(M) with Z(I) compact. Then IZ(I)=I?R, where Z(I) is the zero set of I, IZ(I) the ideal of functions (in O(M)) vanishing on I, and I?R the real radical of I (i.e. the set of functions f in O(M) such that there exist g1,?,gk and an integer p with f2p + g2 1 + ? +g2k ? I). Corollary: Let I be as in Theorem 2. Then IZ(I)=I if and only if I is real (i.e. I=I ? R). The proofs are based on results about extension of orders.
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En línea:
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https://eprints.ucm.es/id/eprint/20069/1/RuizSancho26.pdf
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