RT Journal Article
T1 On the Hilbert 17th problem for global analytic functions
A1 Acquistapace, Francesca
A1 Broglia, Fabrizio
A1 Fernando Galván, José Francisco
A1 Ruiz Sancho, Jesús María
AB 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 thesolution of the problem and the computation of Pythagoras numbers of meromorphic functions
YR 2004
FD 2004-01-26
LK https://hdl.handle.net/20.500.14352/50644
UL https://hdl.handle.net/20.500.14352/50644
LA eng
NO 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).
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RD 3 may 2024