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A short proof of the infinitesimal Hilbertianity of the weighted Euclidean space

dc.contributor.authorDi Marino, Simone
dc.contributor.authorLučić, Danka
dc.contributor.authorPasqualetto, Enrico
dc.date.accessioned2020-12-18T11:05:31Z
dc.date.available2020-12-18T11:05:31Z
dc.date.issued2020
dc.identifier.citationDi Marino, S., Lučić, D., & Pasqualetto, E. (2020). A short proof of the infinitesimal Hilbertianity of the weighted Euclidean space. <i>Comptes Rendus Mathematique</i>, <i>358</i>(7), 817-825. <a href="https://doi.org/10.5802/crmath.88" target="_blank">https://doi.org/10.5802/crmath.88</a>
dc.identifier.otherCONVID_47458421
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/73342
dc.description.abstractWe provide a quick proof of the following known result: the Sobolev space associated with the Euclidean space, endowed with the Euclidean distance and an arbitrary Radon measure, is Hilbert. Our new approach relies upon the properties of the Alberti–Marchese decomposability bundle. As a consequence of our arguments, we also prove that if the Sobolev norm is closable on compactly-supported smooth functions, then the reference measure is absolutely continuous with respect to the Lebesgue measure.en
dc.format.mimetypeapplication/pdf
dc.languageeng
dc.language.isoeng
dc.publisherInstitut de France
dc.relation.ispartofseriesComptes Rendus Mathematique
dc.rightsCC BY 4.0
dc.titleA short proof of the infinitesimal Hilbertianity of the weighted Euclidean space
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202012187289
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineMatematiikkafi
dc.contributor.oppiaineMathematicsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.format.pagerange817-825
dc.relation.issn1631-073X
dc.relation.numberinseries7
dc.relation.volume358
dc.type.versionpublishedVersion
dc.rights.copyright© Académie des sciences, Paris and the authors, 2020
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber274372
dc.relation.grantnumber307333 HY
dc.relation.grantnumber312488
dc.relation.grantnumber314789
dc.subject.ysofunktionaalianalyysi
dc.subject.ysodifferentiaaligeometria
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p17780
jyx.subject.urihttp://www.yso.fi/onto/yso/p16682
dc.rights.urlhttps://creativecommons.org/licenses/by/4.0/
dc.relation.doi10.5802/crmath.88
dc.relation.funderResearch Council of Finlanden
dc.relation.funderResearch Council of Finlanden
dc.relation.funderResearch Council of Finlanden
dc.relation.funderResearch Council of Finlanden
dc.relation.funderSuomen Akatemiafi
dc.relation.funderSuomen Akatemiafi
dc.relation.funderSuomen Akatemiafi
dc.relation.funderSuomen Akatemiafi
jyx.fundingprogramAcademy Research Fellow, AoFen
jyx.fundingprogramCentre of Excellence, AoFen
jyx.fundingprogramResearch costs of Academy Research Fellow, AoFen
jyx.fundingprogramAcademy Project, AoFen
jyx.fundingprogramAkatemiatutkija, SAfi
jyx.fundingprogramHuippuyksikkörahoitus, SAfi
jyx.fundingprogramAkatemiatutkijan tutkimuskulut, SAfi
jyx.fundingprogramAkatemiahanke, SAfi
jyx.fundinginformationThe second and third named authors acknowledge the support by the Academy of Finland, projects 274372, 307333, 312488, and 314789. The first named author is a member of GNAMPA, INdAM.
dc.type.okmA1


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