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Documentos disponibles escritos por este autor (73)
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A set which can be defined by systems of polynomial inequalities is called semialgebraic. When such a scription is possible locally around every point, by means of analytic inequalities varying with the point, the set; is called semianalytic. If[...]texto impreso
A semialgebraic set is called basic if it can be described by a single system of strict polynomial inequalities. A semianalytic set is called basic if it can be described by a system of strict real analytic inequalities in a neighborhood of each[...]texto impreso
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Let ??Rn be a compact Nash manifold; A,B the rings of Nash, analytic global functions on ?. The main result of this paper is the following: Theorem 1. Let ?,?? be a pair of Nash submanifolds of some Rn ,Rq and let us suppose ? is compact. Let F1[...]texto impreso
Baro González, Elías ; Fernando Galván, José Francisco ; Ruiz Sancho, Jesús María | Elsevier | 2014-09This paper is devoted to the approximation of differentiable semialgebraic functions by Nash functions. Approximation by Nash functions is known for semialgebraic functions defined on an affine Nash manifold M, and here we extend it to functions[...]texto impreso
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We give an expository account of the basic features of analytic and semianalytic germs. The main results treated here are Risler's Nullstellensatz, the curve selection lemma and the finiteness theorem for semianalytic germs. The method of proof [...]texto impreso
Abánades, Miguel A. ; Joglar-Prieto, Nuria ; Ruiz Sancho, Jesús María | Elsevier Science B.V. (North-Holland) | 1999-10-01We show that the ring of bounded meromorphic functions on an irreducible compact real analytic set of dimension d is a Prüfer domain of dimension d. Consequently, every finitely generated ideal in this ring can be generated by d + 1 elements, an[...]texto impreso
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The paper deals with orderings in the field K(X0) of meromorphic function germs on an irreducible analytic germ X0?Rn0 of dimension d. It is inspired by the theory of central points of real algebraic varieties (the set of central points is the c[...]texto impreso
Hilbert's 17th Problem asked the following. Let f(x1,?,xn) be a real polynomial which for all real values ?1,?,?n satisfies f(?1,?,?n)?0. Is it true that f=?(gi/hi)2 for polynomials gi,hi?R[x1,?,xn]? (It was known that f=?(gi)2, gi?R[x1,?,xn], i[...]texto impreso
Let A be a local ring; let  denote the completion of A and Spec r A,Spec R  the real spectra of A and Â,respectively. The author studies the fibers of the canonical morphism Spec r  ? Spec r A, for an excellent ring A, and computes its images[...]
