The multidimensional truncated moment problem: Carathéodory numbers from Hilbert functions
| dc.contributor.author | Dio, Philipp J. di | |
| dc.contributor.author | Kummer, Mario | |
| dc.date.accessioned | 2021-05-31T08:40:49Z | |
| dc.date.available | 2021-05-31T08:40:49Z | |
| dc.date.issued | 2021-03-24 | |
| dc.description.abstract | In this paper we improve the bounds for the Carathéodory number, especially on algebraic varieties and with small gaps (not all monomials are present). We provide explicit lower and upper bounds on algebraic varieties, Rn, and [0,1]n. We also treat moment problems with small gaps. We find that for every ε>0 and d∈N there is a n∈N such that we can construct a moment functional L:R[x1,⋯,xn]≤d→R which needs at least (1−ε)⋅(n+dn) atoms lxi. Consequences and results for the Hankel matrix and flat extension are gained. We find that there are moment functionals L:R[x1,⋯,xn]≤2d→R which need to be extended to the worst case degree 4d, L~:R[x1,⋯,xn]≤4d→R, in order to have a flat extension. | en |
| dc.description.sponsorship | TU Berlin, Open-Access-Mittel – 2021 | en |
| dc.identifier.eissn | 1432-1807 | |
| dc.identifier.issn | 0025-5831 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/13167 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-11961 | |
| dc.language.iso | en | en |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | en |
| dc.subject.ddc | 510 Mathematik | de |
| dc.subject.other | Carathéodory numbers | en |
| dc.subject.other | Hilbert functions | en |
| dc.subject.other | multidimensional truncated moment problem | en |
| dc.title | The multidimensional truncated moment problem: Carathéodory numbers from Hilbert functions | en |
| dc.type | Article | en |
| dc.type.version | publishedVersion | en |
| dcterms.bibliographicCitation.doi | 10.1007/s00208-021-02166-x | en |
| dcterms.bibliographicCitation.journaltitle | Mathematische Annalen | en |
| dcterms.bibliographicCitation.originalpublishername | Springer Nature | en |
| dcterms.bibliographicCitation.originalpublisherplace | Heidelberg | en |
| dcterms.bibliographicCitation.pageend | 291 | en |
| dcterms.bibliographicCitation.pagestart | 267 | en |
| dcterms.bibliographicCitation.volume | 380 | en |
| tub.accessrights.dnb | free | en |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |