Nash Functions: Real Algebraic Geometry, Analytic Function, Semialgebraic Set, Implicit Function - Tapa blanda

Nash Functions

Taschenbuch. Condición: Neu. This item is printed on demand - Print on Demand Titel. Neuware -High Quality Content by WIKIPEDIA articles! In real algebraic geometrya Nash function on an open semialgebraic subset U of Rn is an analyticfunction f: U -> R satisfying a non trivial polynomial equationP(x,f(x)) = 0 for all x in U. (A semialgebraic subset of Rn is a subsetobtained from subsets of the form {x in Rn : P(x)=0} or {x in Rn : P(x)> 0}, where P is a polynomial, by taking finite unions, finiteintersections and complements.) Polynomial and regular rationalfunctions are Nash functions; the function xmapsto sqrt{1+x^2} is Nashon R; the function which associates to a real symmetric matrix its i-theigenvalue (in increasing order) is Nash on the open subset of symmetricmatrices with no multiple eigenvalue. Actually, Nash functions are thosefunctions needed in order to have an implicit function theorem in realalgebraic geometry.VDM Verlag, Dudweiler Landstraße 99, 66123 Saarbrücken 72 pp. Englisch. Nº de ref. del artículo: 9786131298332

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