The strict Positivstellensatz for global analytic functions and the moment problem for semianalytic sets
| dc.contributor.author | Acquistapace, Francesca | |
| dc.contributor.author | Andradas Heranz, Carlos | |
| dc.contributor.author | Broglia, Fabrizio | |
| dc.date.accessioned | 2023-06-20T16:49:41Z | |
| dc.date.available | 2023-06-20T16:49:41Z | |
| dc.date.issued | 2000 | |
| dc.description.abstract | Analytic functions strictly positive on a global semianalytic set X = {f1 0, · · · , fk 0} in Rn are characterized as functions expressible as g = a0+a1f1+· · ·+akfk for strictly positive global analytic functions a0, · · · , ak. The proof is elementary, using the fact that the analytic functions are dense in C(Rn,R) in the Whitney topology. The same proof works for Nash functions. This is an improvement of the standard analytic version of Stengle’s Positivstellensatz in two directions: The hypothesis is weaker (there is no requirement that X be compact) and the conclusion is stronger. Several applications are given including: (i) a new proof of the weak Positivstellensatz for semianalytic sets; and (ii) the solution of theK-moment problem for basic closed semianalytic | |
| 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 | CNR | |
| dc.description.sponsorship | MURST | |
| dc.description.sponsorship | DGES | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/14797 | |
| dc.identifier.doi | 10.1007/s002080050346 | |
| dc.identifier.issn | 0025-5831 | |
| dc.identifier.officialurl | http://www.springerlink.com/content/4pq0j27lr3k08e5l/fulltext.pdf | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57155 | |
| dc.issue.number | 4 | |
| dc.journal.title | Mathematische Annalen | |
| dc.language.iso | eng | |
| dc.page.final | 616 | |
| dc.page.initial | 606 | |
| dc.publisher | Springer | |
| dc.relation.projectID | HI1997-0122 | |
| dc.relation.projectID | PB95-0354 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 512.7 | |
| dc.subject.keyword | Positivstellensatz | |
| dc.subject.keyword | global semianalytic set | |
| dc.subject.keyword | K-moment problem Classification | |
| dc.subject.ucm | Geometria algebraica | |
| dc.subject.unesco | 1201.01 Geometría Algebraica | |
| dc.title | The strict Positivstellensatz for global analytic functions and the moment problem for semianalytic sets | |
| dc.type | journal article | |
| dc.volume.number | 316 | |
| dcterms.references | [ABR] C. Andradas, L.Br¨ocker, J.M.Ruiz. Constructible sets in real geometry. Ergeb. Math. Greuzgeb (3) 33 Berlin Springer Verlag (1996) [BCR] J. Bochnack, M.Coste, M.F.Roy. Real algebraic geometry. Ergeb. Math. Greuzgeb (3) 36 Berlin Springer Verlag (1998) [BS] E. Becker, N. Schwartz. Zum Darstellungsatz von Kadison–Dubois. Archiv der Math. Vol. 40 (1983),421–428 [BW] R. Berr, T.W¨orman. Positive polynomials and tame preorderings. Preprint (1998) [C] G. Choquet.Lectures on analysis. Vol. 1 Reading; Benjamin (1969) [J] T. Jacobi. A representation theorem for certain partially ordered commutative rings. To appear. [M] M.A. Marshall. A real holomorphy ring without the Schm¨udgen property. Canad. Math. Bull. 42(3), 354–358 (1999) [N] R. Narasimhan. Analysis on real and complex manifolds. Masson & cie, Paris; North- Holland, Amsterdam (1968) [P] M. Putinar. Positive Polynomials on Compact Semi-algebraic Sets. Indiana Univ. math. Journ. Vol. 42 No. 3 969–984 (1993) [S] K. Schm¨udgen. The K–moment problem for compact semi–algebraic sets. Math. Ann. 289, 203–206 (1991) [Sh] M. Shiota. Nash Manifolds. Lect. Notes in Math. 1269. Berlin: Springer-Verlag (1987) [W] T.W¨ormann. Short algebraic proofs of theorems of Schm¨udgen and P´olya. to appear | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | a74c23fe-4059-4e73-806b-71967e14ab67 | |
| relation.isAuthorOfPublication.latestForDiscovery | a74c23fe-4059-4e73-806b-71967e14ab67 |
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