Where do homogeneous polynomials on ln1 attain their norm?

Villanueva Díez, Ignacio; Pérez García, David

doi:10.1016/j.jat.2004.01.001

Where do homogeneous polynomials on ln1 attain their norm?

dc.contributor.author	Villanueva Díez, Ignacio
dc.contributor.author	Pérez García, David
dc.date.accessioned	2023-06-20T09:25:21Z
dc.date.available	2023-06-20T09:25:21Z
dc.date.issued	2004-03-01
dc.description.abstract	Using a ‘reasonable’ measure in , the space of 2-homogeneous polynomials on ℓ1n, we show the existence of a set of positive (and independent of n) measure of polynomials which do not attain their norm at the vertices of the unit ball of ℓ1n. Next we prove that, when n grows, almost every polynomial attains its norm in a face of ‘low’ dimension.	en
dc.description.department	Depto. de Análisis Matemático y Matemática Aplicada
dc.description.faculty	Fac. de Ciencias Matemáticas
dc.description.refereed	TRUE
dc.description.sponsorship	Dirección General de Investigación Científica y Técnica (España)
dc.description.status	pub
dc.eprint.id	https://eprints.ucm.es/id/eprint/11658
dc.identifier.citation	Pérez Garcı́a, D. & Villanueva Díez, I. «Where Do Homogeneous Polynomials on ℓ1n Attain Their Norm?» Journal of Approximation Theory, vol. 127, n.o 1, marzo de 2004, pp. 124-33. DOI.org (Crossref), https://doi.org/10.1016/j.jat.2004.01.001.
dc.identifier.doi	10.1016/j.jat.2004.01.001
dc.identifier.issn	1096-0430
dc.identifier.officialurl	https//doi.org/10.1016/j.jat.2004.01.001
dc.identifier.relatedurl	http://www.sciencedirect.com/science/journal/00219045
dc.identifier.uri	https://hdl.handle.net/20.500.14352/49447
dc.issue.number	1
dc.journal.title	Journal of Approximation Theory
dc.language.iso	eng
dc.page.final	133
dc.page.initial	124
dc.publisher	Elsevier
dc.relation.projectID	(BMF2001-1284)
dc.rights.accessRights	open access
dc.subject.cdu	517
dc.subject.keyword	Polynomials
dc.subject.keyword	Extreme points
dc.subject.keyword	Convex polytopes
dc.subject.keyword	Vertices
dc.subject.keyword	Faces
dc.subject.ucm	Análisis matemático
dc.subject.unesco	1202 Análisis y Análisis Funcional
dc.title	Where do homogeneous polynomials on ln1 attain their norm?	en
dc.type	journal article
dc.volume.number	127
dspace.entity.type	Publication
relation.isAuthorOfPublication	45785a65-66ff-415c-a422-bfdc6e3ff149
relation.isAuthorOfPublication	5edb2da8-669b-42d1-867d-8fe3144eb216
relation.isAuthorOfPublication.latestForDiscovery	5edb2da8-669b-42d1-867d-8fe3144eb216

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