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dc.contributor.authorLuca, R.
dc.contributor.authorPonce-Vanegas, F.
dc.date.accessioned2021-01-19T07:41:45Z
dc.date.available2021-01-19T07:41:45Z
dc.date.issued2021-01
dc.identifier.urihttp://hdl.handle.net/20.500.11824/1240
dc.description.abstractWe consider a fractal refinement of the Carleson problem for the Schrödinger equation, that is to identify the minimal regularity needed by the solutions to converge pointwise to their initial data almost everywhere with respect to the $\alpha$-Hausdorff measure ($\alpha$-a.e.). We extend to the fractal setting ($\alpha < n$) a recent counterexample of Bourgain \cite{Bourgain2016}, which is sharp in the Lebesque measure setting ($\alpha = n$). In doing so we recover the necessary condition from \cite{zbMATH07036806} for pointwise convergence~$\alpha$-a.e. and we extend it to the range $n/2<\alpha \leq (3n+1)/4$.en_US
dc.description.sponsorshipIkerbasqueen_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectSchrödinger equationen_US
dc.subjectpointwise convergenceen_US
dc.subjectfractalen_US
dc.titleConvergence over fractals for the Schrödinger equationen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/H2020/669689en_US
dc.relation.projectIDES/1PE/SEV-2017-0718en_US
dc.relation.projectIDES/2PE/PGC2018-094528-B-I00en_US
dc.relation.projectIDEUS/BERC/BERC.2018-2021en_US
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/submittedVersionen_US


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