On Hilbert's 17th Problem for global analytic functions indimension 3.
| dc.contributor.author | Fernando Galván, José Francisco | |
| dc.date.accessioned | 2023-06-20T09:33:28Z | |
| dc.date.available | 2023-06-20T09:33:28Z | |
| dc.date.issued | 2008 | |
| dc.description.abstract | Among the invariant factors g of a positive semidefinite analytic function f on R-3, those g whose zero set Y is a curve are called special. We show that if each special g is a sum of squares of global meromorphic functions on a neighbourhood of Y, then f is a sum of squares of global meromorphic functions. Here sums can be (convergent) infinite, but we also find some sufficient conditions to get finite sums of squares. In addition, we construct several examples of positive semidefinite analytic functions which are infinite sums of squares but maybe could not be finite sums of squares. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | GAAR | |
| dc.description.sponsorship | GAAR | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/15125 | |
| dc.identifier.doi | 10.4171/CMH/119 | |
| dc.identifier.issn | 0010-2571 | |
| dc.identifier.officialurl | http://www.ems-ph.org/journals/show_abstract.php?issn=0010-2571&vol=83&iss=1&rank=5 | |
| dc.identifier.relatedurl | http://www.ems.org | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/49897 | |
| dc.issue.number | 1 | |
| dc.journal.title | Commentarii Mathematici Helvetici | |
| dc.language.iso | eng | |
| dc.page.final | 100 | |
| dc.page.initial | 67 | |
| dc.publisher | European Mathematical Society | |
| dc.relation.projectID | BFM2002-04797 | |
| dc.relation.projectID | UCM 910444. | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 511 | |
| dc.subject.keyword | Hilbert’s 17th Problem | |
| dc.subject.keyword | Sum of squares | |
| dc.subject.keyword | Irreducible factors | |
| dc.subject.keyword | Special factors. | |
| dc.subject.ucm | Teoría de números | |
| dc.subject.unesco | 1205 Teoría de Números | |
| dc.title | On Hilbert's 17th Problem for global analytic functions indimension 3. | |
| dc.type | journal article | |
| dc.volume.number | 83 | |
| dcterms.references | F. Acquistapace, F. Broglia, J. F. Fernando, J. M. Ruiz, On the finiteness of Pythagoras numbers of real meromorphic functions.Talk at theRAAGannual meeting, Salamanca, Spain, 2004. http://www.uni-regensburg.de/Fakultaeten/nat Fak_I/RAAG/preprints/0185.pdf C. Andradas, L. Bröcker, J. M. Ruiz, Constructible Sets in Real Geometry. Ergeb. Math. Grenzgeb. 33, Springer-Verlag, Berlin 1996. Zbl 0873.14044 MR 1393194 E. Artin, Über die Zerlegung definiter Funktionen in Quadrate. Hamb. Abh. 5 (1927), 100–115; The collected papers of Emil Artin, Addison-Wesley, Reading, MA, 1965, 273–288. JFM 52.0122.01 J. Bochnak, M. Coste, M. F. Roy, Real Algebraic Geometry. Ergeb. Math. Grenzgeb. 36, Springer-Verlag, Berlin 1998. Zbl 0912.14023 MR 1659509 J. Bochnak, W. Kucharz, M. Shiota, On equivalence of ideals of real global analytic functions and the 17th Hilbert problem. Invent. Math. 63 (1981), 403–421. Zbl 0467.32003 MR 0620677 H. Cartan, Variétés analytiques réelles et variétés analytiques complexes. Bull. Soc. Math. France 85 (1957), 77–99. Zbl 0083.30502 MR 0094830 R. Gunning, H. Rossi, Analytic functions of several complex variables. Prentice Hall, Englewood Cliff, N.J., 1965. Zbl 0141.08601 MR 0180696 P. Jaworski, Positive definite analytic functions and vector bundles. Bull. Acad. Polon. Sci. Sér. Sci. Math. 30 (1982), 501–506. Zbl 0554.32006 MR 0718726 P. Jaworski, Extension of orderings on fields of quotients of rings of real analytic functions. Math. Nachr. 125 (1986), 329–339. Zbl 0601.14018 MR 0847371 T. Y. Lam, The Algebraic Theory of Quadratic Forms. Mathematics Lecture Notes Series,W. A. Benjaming, Inc., Reading, MA, 1973. Zbl 0259.10019 MR 0396410 A. Pfister, Quadratic Forms with Applications to Algebraic Geometry and Topology. London Math. Soc. Lect. Notes Ser. 217, Cambridge University Press, Cambridge 1995. Zbl 0847.11014 MR 1366652 J. M. Ruiz, On Hilbert’s 17th problem and real Nullstellensatz for global analytic functions. Math. Z. 190 (1985), 447–454. Zbl 0579.14021 MR 0806902 H. Whitney, F. Bruhat, Quelques propiétés fondamentales des ensembles analytiques réels. Comment. Math. Helv. 33 (1959), 132–160. Zbl 0100.08101 MR 0102094 | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 499732d5-c130-4ea6-8541-c4ec934da408 | |
| relation.isAuthorOfPublication.latestForDiscovery | 499732d5-c130-4ea6-8541-c4ec934da408 |
Download
Original bundle
1 - 1 of 1