On the Hilbert 17th problem for global analytic functions
| dc.contributor.author | Acquistapace, Francesca | |
| dc.contributor.author | Broglia, Fabrizio | |
| dc.contributor.author | Fernando Galván, José Francisco | |
| dc.contributor.author | Ruiz Sancho, Jesús María | |
| dc.date.accessioned | 2023-06-20T10:34:57Z | |
| dc.date.available | 2023-06-20T10:34:57Z | |
| dc.date.issued | 2004-01-26 | |
| dc.description.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 | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | FALSE | |
| dc.description.sponsorship | European RAAG | |
| dc.description.sponsorship | Italian GNSAGA of INdAM and MIUR | |
| dc.description.sponsorship | Spanish GAAR | |
| dc.description.status | submitted | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/21367 | |
| dc.identifier.officialurl | http://www.maths.manchester.ac.uk/raag/index.php?preprint=0083 | |
| dc.identifier.relatedurl | http://www.maths.manchester.ac.uk | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/50644 | |
| dc.journal.title | Real algebraic and analytic geometry: preprint server | |
| dc.language.iso | eng | |
| dc.page.final | 31 | |
| dc.page.initial | 1 | |
| dc.relation.projectID | HPRN-CT-2001-0027 | |
| dc.relation.projectID | BFM-2002-04797 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 512.7 | |
| dc.subject.keyword | Hilbert 17th Problem | |
| dc.subject.keyword | Pythagoras number | |
| dc.subject.keyword | sum of squares | |
| dc.subject.keyword | bad set | |
| dc.subject.keyword | germs at closed sets | |
| dc.subject.ucm | Geometria algebraica | |
| dc.subject.unesco | 1201.01 Geometría Algebraica | |
| dc.title | On the Hilbert 17th problem for global analytic functions | |
| dc.type | journal article | |
| dc.volume.number | 83 | |
| dcterms.references | 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). | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 499732d5-c130-4ea6-8541-c4ec934da408 | |
| relation.isAuthorOfPublication | f12f8d97-65c7-46aa-ad47-2b7099b37aa4 | |
| relation.isAuthorOfPublication.latestForDiscovery | 499732d5-c130-4ea6-8541-c4ec934da408 |
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