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Continuous valuations on the space of Lipschitz on the sphere

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dc.contributor.authorColesanti, Andrea
dc.contributor.authorPagnini, Daniele
dc.contributor.authorTradacete Pérez, Pedro
dc.contributor.authorVillanueva Díez, Ignacio
dc.date.accessioned2023-06-17T08:29:00Z
dc.date.available2023-06-17T08:29:00Z
dc.date.issued2020-11-30
dc.description.abstractWe study real-valued valuations on the space of Lipschitz functions over the Euclidean unit sphere Sn−1. After introducing an appropriate notion of convergence, we show that continuous valuations are bounded on sets which are bounded with respect to the Lipschitz norm. This fact, in combination with measure theoretical arguments, will yield an integral representation for continuous and rotation invariant valuations on the space of Lipschitz functions over the 1-dimensional sphere. Contentsen
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedFALSE
dc.description.sponsorshipMinisterio de Ciencia, Innovación y Universidades (España)/Fondo Europeo de Desarrollo Regional
dc.description.sponsorshipMinisterio de Economía, Comercio y Empresa (España)
dc.description.sponsorshipComunidad de Madrid
dc.description.sponsorshipCentro de Excelencia Severo Ochoa
dc.description.sponsorshipUniversidad Complutense de Madrid
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/74378
dc.identifier.citationColesanti, A., Pagnini, D., Tradacete Pérez, P. et al. «Continuous Valuations on the Space of Lipschitz Functions on the Sphere». Journal of Functional Analysis, vol. 280, n.o 4, febrero de 2021, p. 108873. DOI.org (Crossref), https://doi.org/10.1016/j.jfa.2020.108873.
dc.identifier.doi10.1016/j.jfa.2020.108873
dc.identifier.issn0022-1236
dc.identifier.officialurlhttps://doi.org/10.1016/j.jfa.2020.108873
dc.identifier.urihttps://hdl.handle.net/20.500.14352/7253
dc.issue.number4
dc.journal.titleJournal of functional analysis
dc.language.isoeng
dc.publisherElsevier
dc.relation.projectIDMTM2016-76808-P
dc.relation.projectIDMTM2017-88385-P
dc.relation.projectIDQUITEMAD+-CM (S2013/ICE-2801)
dc.relation.projectID(SEV-2015-0554; 20205CEX001)
dc.relation.projectIDUCM (910346)
dc.rights.accessRightsopen access
dc.subject.cdu517
dc.subject.keywordGeometric valuation Theory
dc.subject.keywordLipschitz functions
dc.subject.keywordIntegral representation
dc.subject.ucmAnálisis matemático
dc.subject.unesco1202 Análisis y Análisis Funcional
dc.titleContinuous valuations on the space of Lipschitz on the sphereen
dc.typejournal article
dc.volume.number280
dspace.entity.typePublication
relation.isAuthorOfPublication45785a65-66ff-415c-a422-bfdc6e3ff149
relation.isAuthorOfPublication.latestForDiscovery45785a65-66ff-415c-a422-bfdc6e3ff149

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