The multidimensional truncated moment problem: Carathéodory numbers from Hilbert functions

dc.contributor.authorDio, Philipp J. di
dc.contributor.authorKummer, Mario
dc.date.accessioned2021-05-31T08:40:49Z
dc.date.available2021-05-31T08:40:49Z
dc.date.issued2021-03-24
dc.description.abstractIn 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.sponsorshipTU Berlin, Open-Access-Mittel – 2021en
dc.identifier.eissn1432-1807
dc.identifier.issn0025-5831
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/13167
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-11961
dc.language.isoenen
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en
dc.subject.ddc510 Mathematikde
dc.subject.otherCarathéodory numbersen
dc.subject.otherHilbert functionsen
dc.subject.othermultidimensional truncated moment problemen
dc.titleThe multidimensional truncated moment problem: Carathéodory numbers from Hilbert functionsen
dc.typeArticleen
dc.type.versionpublishedVersionen
dcterms.bibliographicCitation.doi10.1007/s00208-021-02166-xen
dcterms.bibliographicCitation.journaltitleMathematische Annalenen
dcterms.bibliographicCitation.originalpublishernameSpringer Natureen
dcterms.bibliographicCitation.originalpublisherplaceHeidelbergen
dcterms.bibliographicCitation.pageend291en
dcterms.bibliographicCitation.pagestart267en
dcterms.bibliographicCitation.volume380en
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
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