The Positivstellensatz for definable functions on O-minimal structures
| dc.contributor.author | Acquistapace, Francesca | |
| dc.contributor.author | Andradas Heranz, Carlos | |
| dc.contributor.author | Broglia, Fabrizio | |
| dc.date.accessioned | 2023-06-20T16:49:38Z | |
| dc.date.available | 2023-06-20T16:49:38Z | |
| dc.date.issued | 2002 | |
| dc.description.abstract | In this note we prove two Positivstellensatze for definable functions of class C-r, 0 less than or equal to r < &INFIN;, in any o-minimal structure S expanding a real closed field R. Namely, we characterize the definable functions that are nonnegative (resp. strictly positive) on basic definable sets of the form F = {f(1) &GE; 0,...,f(k) &GE; 0}. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | GNSAGA | |
| dc.description.sponsorship | DGES | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/14764 | |
| dc.identifier.issn | 0019-2082 | |
| dc.identifier.officialurl | https://www.projecteuclid.org/euclid.ijm/1258130979 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57152 | |
| dc.issue.number | 3 | |
| dc.journal.title | Illinois Journal of Mathematics | |
| dc.language.iso | eng | |
| dc.page.final | 693 | |
| dc.page.initial | 685 | |
| dc.publisher | University of Illinois | |
| dc.relation.projectID | PB98-0756-C02-01 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 512.7 | |
| dc.subject.keyword | Positivstellensatz | |
| dc.subject.keyword | definable functions | |
| dc.subject.keyword | o-minimal structure | |
| dc.subject.keyword | real closed field | |
| dc.subject.ucm | Geometria algebraica | |
| dc.subject.unesco | 1201.01 Geometría Algebraica | |
| dc.title | The Positivstellensatz for definable functions on O-minimal structures | |
| dc.type | journal article | |
| dc.volume.number | 46 | |
| dcterms.references | [AAB] F. Acquistapace, C. Andradas, and F. Broglia, The strict Positivstellensatz for global analytic functions and the moment problem for semianalytic sets, Math. Ann. 316 (2000), 609{616. [BCR] J. Bochnack, M. Coste, and M. F. Roy, Real algebraic geometry, Ergeb. Math. Grenzgebiete (3), vol. 36, Springer-Verlag, Berlin, 1998. [Br] G. W. Brumel, Partially ordered rings and semi-algebraic geometry, London Math. Soc. Lecture Note Series, vol. 37, Cambridge University Press, Cambridge, 1978. [Co] M. Coste, An Introduction to o-minimal geometry. Dpto. di Matematica Univ. di Pisa, 2000. [De] C. Delzell, A constructive, continuous solution to Hilbert's 17th Problem and other results in semialgebraic geometry, PhD. Dissertation, Stanford Univ., 1980. [Dr] L. van den Dries, Tame topology and o-minimal structures, London Math. Soc. Lecture Note Series, vol. 248, Cambridge Univ. Press, Cambridge, 1998. [DMi] L. van den Dries and C. Miller, Geometric categories and o-minimal structures, Duke Math. J. 84 (2) (1996), 497{540. [Es] J. Escribano, Ph.D. Thesis, Univ. Complutense de Madrid, 2000. [Mo] T. S. Motzkin, The arithmetic-geometric inequality, Inequalities (Proc. Sympos. Wright-Patterson Air Force Base, Ohio, 1965), Academic Press, New York, 1967, pp. 205{224. [Pu] M. Putinar, Positive polynomials on compact semialgebraic sets, Indiana Univ. Math. J. 42 (1993), 969{984. [Sche] C. Scheiderer, Sums of squares of regular functions on real algebraic varieties, Trans. Amer. Math. Soc. 352 (2000), 1039{1069. [Schm] K. Schm�udgen, The K{moment problem for compact semi{algebraic sets, Math. Ann. 289 (1991), 203{206. [St] G. Stengle, A Nullstellensatz and a Positivstellensatz in semialgebraic geometry, Math. Ann. 207 (1974), 87{97. [To] J. C. Tougeron, Ideaux de fonctions dierentiables, Ergeb. Math. Grenzgebiete, vol. 71, Springer-Verlag, Berlin, 1972. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | a74c23fe-4059-4e73-806b-71967e14ab67 | |
| relation.isAuthorOfPublication.latestForDiscovery | a74c23fe-4059-4e73-806b-71967e14ab67 |
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