Publication:
Decoupling for fractal subsets of the parabola

dc.contributor.coauthorChang, Alan
dc.contributor.coauthorPont, Jaume de Dios
dc.contributor.coauthorGreenfeld, Rachel
dc.contributor.coauthorLi, Zane Kun
dc.contributor.coauthorMadrid, Jose
dc.contributor.departmentDepartment of Mathematics
dc.contributor.kuauthorJamneshan, Asgar
dc.contributor.schoolcollegeinstituteCollege of Sciences
dc.date.accessioned2024-11-09T12:33:38Z
dc.date.issued2022
dc.description.abstractWe consider decoupling for a fractal subset of the parabola. We reduce studying l(2)L(p) dccoupling for a fractal subset on the parabola {(t , t(2)) : 0 <= t <= 1} to studying l(2)L(p/3) decoupling for the projection of this subset to the interval [0, 1]. This generalizes the decoupling theorem of Bourgain-Demeter in the case of the parabola. Due to the sparsity and fractal like structure, this allows us to improve upon Bourgain-Demeter's decoupling theorem for the parabola. In the case when p/3 is an even integer we derive theoretical and computational tools to explicitly compute the associated decoupling constant for this projection to [0, 1]. Our ideas are inspired by the recent work on ellipsephic sets by Biggs (arXiv:1912.04351, 2019 and Acta Arith. 200(4):331-348, 2021) using nested efficient congruencing.
dc.description.fulltextYES
dc.description.indexedbyWOS
dc.description.indexedbyScopus
dc.description.issue2
dc.description.openaccessYES
dc.description.publisherscopeInternational
dc.description.sponsoredbyTubitakEuN/A
dc.description.sponsorshipLa Caixa Foundation “La Caixa” Fellowship
dc.description.sponsorshipEric and Wendy Schmidt Postdoctoral Award
dc.description.sponsorshipGerman Research Foundation (DFG)
dc.description.sponsorshipNational Science Foundation (NSF)
dc.description.versionAuthor's final manuscript
dc.description.volume301
dc.identifier.doi10.1007/s00209-021-02950-0
dc.identifier.eissn1432-1823
dc.identifier.embargoNO
dc.identifier.filenameinventorynoIR03596
dc.identifier.issn0025-5874
dc.identifier.quartileQ3
dc.identifier.scopus2-s2.0-85124180544
dc.identifier.urihttps://doi.org/10.1007/s00209-021-02950-0
dc.identifier.wos750679200001
dc.keywordsHausdorff dimension
dc.keywordsOscillatory integrals
dc.keywordsKakeya set
dc.language.isoeng
dc.publisherSpringer Nature
dc.relation.grantnoLCF/BQ/AA17/11610013
dc.relation.grantnoJA 2512/3-1
dc.relation.grantnoDMS-1902763
dc.relation.ispartofMathematische Zeitschrift
dc.relation.urihttp://cdm21054.contentdm.oclc.org/cdm/ref/collection/IR/id/10452
dc.subjectMathematics
dc.titleDecoupling for fractal subsets of the parabola
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.kuauthorJamneshan, Asgar
local.publication.orgunit1College of Sciences
local.publication.orgunit2Department of Mathematics
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