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dc.contributor.author
Shmerkin, Pablo Sebastian
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dc.contributor.author
Solomyak, Boris
dc.date.available
2019-11-28T19:27:54Z
dc.date.issued
2016-07
dc.identifier.citation
Shmerkin, Pablo Sebastian; Solomyak, Boris; Absolute continuity of self-similar measures, their projections and convolutions; American Mathematical Society; Transactions Of The American Mathematical Society; 368; 7; 7-2016; 5125-5151
dc.identifier.issn
0002-9947
dc.identifier.uri
http://hdl.handle.net/11336/90812
dc.description.abstract
We show that in many parametrized families of self-similar measures, their projections, and their convolutions, the set of parameters for which the measure fails to be absolutely continuous is very small—of co-dimension at least 1 in parameter space. This complements an active line of research concerning similar questions for dimension. Moreover, we establish some regularity of the density outside this small exceptional set, which applies in particular to Bernoulli convolutions; along the way, we prove some new results about the dimensions of self-similar measures and the absolute continuity of the convolution of two measures. As a concrete application, we obtain a very strong version of Marstrand’s projection theorem for planar self-similar sets.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
American Mathematical Society
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dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
ABSOLUTE CONTINUITY
dc.subject
SELF-SIMILAR MEASURES
dc.subject
HAUSDORFF DIMENSION
dc.subject
CONVOLUTIONS
dc.subject.classification
Matemática Pura
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dc.subject.classification
Matemáticas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
Absolute continuity of self-similar measures, their projections and convolutions
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2019-11-21T17:36:43Z
dc.journal.volume
368
dc.journal.number
7
dc.journal.pagination
5125-5151
dc.journal.pais
Estados Unidos
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dc.journal.ciudad
Providence
dc.description.fil
Fil: Shmerkin, Pablo Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina
dc.description.fil
Fil: Solomyak, Boris. University of Washington; Estados Unidos
dc.journal.title
Transactions Of The American Mathematical Society
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dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/tran/2016-368-07/S0002-9947-2015-06696-3/
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1090/tran6696
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