Publication: On the Hilbert 17th problem for global analytic functions
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Publication Date
2004-01-26
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Abstract
We consider Hilbert’s 17 problem for global analytic functions in a modified form that involves infinite sums of squares. This reveals an essential connection between the
solution of the problem and the computation of Pythagoras numbers of meromorphic functions
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C. Andradas, L. Bröcker, J.M. Ruiz: Constructible Sets in Real Geometry, Ergeb. Math. Grenzgeb. 33. Berlin Heidelberg New York: Springer Verlag, 1996.
J. Bochnak, M. Coste, M.F. Roy: Real Algebraic Geometry, Ergeb. Math. Grenzgeb. 36. Berlin Heidelberg New York: Springer-Verlag, 1998.
J. Bochnak, W. Kucharz, M. Shiota: On equivalence of ideals of real global analytic functions and the 17th Hilbert problem, Invent. Math. 63, 403-421 (1981).
H. Cartan: Variétés analytiques réelles et variétés analytiques complexes. Bull. Soc. Math. France 85, 77-99 (1957).
S. Coen: Sul rango dei fasci coerenti, Boll. Un. Mat. Ital. 22 373-383 (1967).
Ch.N. Delzell: A constructible continuous solution to Hilbert’s 17th problem, and other results in real Algebraic Geometry. Ph. D. Dissertation, Stanford 1980.
R. Gunning, H. Rossi: Analytic functions of several complex variables. Englewood Cliff: Prentice Hall, 1965.
P. Jaworski: Extension of orderings on fields of quotients of rings of real analytic functions. Math. Nachr. 125, 329-339 (1986).
R. Narasimhan: Analysis on Real and Complex Manifolds, Advances Stuidies in Pure Mathematics, Masson & Cie, Editeur-Paris; Noth-Holland Publishing Company Amsterdam (1968).
J.M. Ruiz: On Hilbert’s 17th problem and real Nullstellensatz for global analytic functions. Math. Z. 190, 447-459 (1985).
H.H. Schaefer: Topological vector spaces. Graduate Texts in Mathematics 3, Springer-Verlag, New York-Berlin, 1971.
H. Whitney, F. Bruhat: Quelques propiétés fondamentales des ensembles analytiques réels. Comment. Math. Helv. 33, 132-160 (1959).