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dc.contributor.authorFalconer, Kenneth John
dc.contributor.editorRuiz, Patricia Alonso
dc.contributor.editorChen, Joe P
dc.contributor.editorRogers, Luke G
dc.contributor.editorStrichartz, Robert S
dc.contributor.editorTeplyaev, Alexander
dc.date.accessioned2021-02-20T00:36:56Z
dc.date.available2021-02-20T00:36:56Z
dc.date.issued2020-03
dc.identifier256667660
dc.identifierac465db3-7376-4ff7-8a95-72ef872f62f8
dc.identifier85115682520
dc.identifier.citationFalconer , K J 2020 , A capacity approach to box and packing dimensions of projections and other images . in P A Ruiz , J P Chen , L G Rogers , R S Strichartz & A Teplyaev (eds) , Analysis, Probability and Mathematical Physics on Fractals . Fractals and Dynamics in Mathematics, Science and the Arts: Theory and Applications , vol. 5 , World Scientific Publishing , Singapore , 6th Cornell Conference on Analysis, Probability, and Mathematical Physics on Fractals , Cornell , New York , United States , 13/06/17 . https://doi.org/10.1142/11696en
dc.identifier.citationconferenceen
dc.identifier.isbn9789811215520
dc.identifier.isbn9789811215537
dc.identifier.isbn9789811215544
dc.identifier.issn2382-6320
dc.identifier.otherORCID: /0000-0001-8823-0406/work/71954856
dc.identifier.urihttps://hdl.handle.net/10023/21467
dc.description.abstractDimension profiles were introduced by Falconer and Howroyd to provide formulae for the box-counting and packing dimensions of the orthogonal projections of a set E or a measure on Euclidean space onto almost all m-dimensional subspaces. The original definitions of dimension profiles are somewhat awkward and not easy to work with. Here we rework this theory with an alternative definition of dimension profiles in terms of capacities of E with respect to certain kernels, and this leads to the box-counting dimensions of projections and other images of sets relatively easily. We also discuss other uses of the profiles, such as the information they give on exceptional sets of projections and dimensions of images under certain stochastic processes. We end by relating this approach to packing dimension.
dc.format.extent14
dc.format.extent276851
dc.language.isoeng
dc.publisherWorld Scientific Publishing
dc.relation.ispartofAnalysis, Probability and Mathematical Physics on Fractalsen
dc.relation.ispartofseriesFractals and Dynamics in Mathematics, Science and the Arts: Theory and Applicationsen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleA capacity approach to box and packing dimensions of projections and other imagesen
dc.typeConference itemen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doi10.1142/11696
dc.date.embargoedUntil2021-02-20
dc.identifier.urlhttps://arxiv.org/abs/1711.05316en


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