Self-similar measures: asymptotic bounds for the dimension and Fourier decay of smooth images

Autores
Mosquera, Carolina Alejandra; Shmerkin, Pablo Sebastian
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
R. Kaufman and M. Tsujii proved that the Fourier transform of self-similar measures has a power decay outside of a sparse set of frequencies. We present a version of this result for homogeneous self-similar measures, with quantitative estimates, and derive several applications: (1) non-linear smooth images of homogeneous self-similar measures have a power Fourier decay, (2) convolving with a homogeneous self-similar measure increases correlation dimension by a quantitative amount, (3) the dimension and Frostman exponent of (biased) Bernoulli convolutions tend to 1 as the contraction ratio tends to 1, at an explicit quantitative rate.
Fil: Mosquera, Carolina Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Fourier decay
self-similar measures
correlation dimension
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/117954
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Self-similar measures: asymptotic bounds for the dimension and Fourier decay of smooth imagesMosquera, Carolina AlejandraShmerkin, Pablo SebastianFourier decayself-similar measurescorrelation dimensionhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1R. Kaufman and M. Tsujii proved that the Fourier transform of self-similar measures has a power decay outside of a sparse set of frequencies. We present a version of this result for homogeneous self-similar measures, with quantitative estimates, and derive several applications: (1) non-linear smooth images of homogeneous self-similar measures have a power Fourier decay, (2) convolving with a homogeneous self-similar measure increases correlation dimension by a quantitative amount, (3) the dimension and Frostman exponent of (biased) Bernoulli convolutions tend to 1 as the contraction ratio tends to 1, at an explicit quantitative rate.Fil: Mosquera, Carolina Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaSuomalainen Tiedeakatemia2018-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfhttp://hdl.handle.net/11336/117954Mosquera, Carolina Alejandra; Shmerkin, Pablo Sebastian; Self-similar measures: asymptotic bounds for the dimension and Fourier decay of smooth images; Suomalainen Tiedeakatemia; Annales Academiae Scientiarum Fennicae. Mathematica; 43; 2; 2-2018; 823-8341239-629X1798-2383CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.acadsci.fi/mathematica/info:eu-repo/semantics/altIdentifier/url/http://www.acadsci.fi/mathematica/Vol43/FengKaenmaki.htmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:50:13Zoai:ri.conicet.gov.ar:11336/117954instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-15 14:50:13.795CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Self-similar measures: asymptotic bounds for the dimension and Fourier decay of smooth images
title Self-similar measures: asymptotic bounds for the dimension and Fourier decay of smooth images
spellingShingle Self-similar measures: asymptotic bounds for the dimension and Fourier decay of smooth images
Mosquera, Carolina Alejandra
Fourier decay
self-similar measures
correlation dimension
title_short Self-similar measures: asymptotic bounds for the dimension and Fourier decay of smooth images
title_full Self-similar measures: asymptotic bounds for the dimension and Fourier decay of smooth images
title_fullStr Self-similar measures: asymptotic bounds for the dimension and Fourier decay of smooth images
title_full_unstemmed Self-similar measures: asymptotic bounds for the dimension and Fourier decay of smooth images
title_sort Self-similar measures: asymptotic bounds for the dimension and Fourier decay of smooth images
dc.creator.none.fl_str_mv Mosquera, Carolina Alejandra
Shmerkin, Pablo Sebastian
author Mosquera, Carolina Alejandra
author_facet Mosquera, Carolina Alejandra
Shmerkin, Pablo Sebastian
author_role author
author2 Shmerkin, Pablo Sebastian
author2_role author
dc.subject.none.fl_str_mv Fourier decay
self-similar measures
correlation dimension
topic Fourier decay
self-similar measures
correlation dimension
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv R. Kaufman and M. Tsujii proved that the Fourier transform of self-similar measures has a power decay outside of a sparse set of frequencies. We present a version of this result for homogeneous self-similar measures, with quantitative estimates, and derive several applications: (1) non-linear smooth images of homogeneous self-similar measures have a power Fourier decay, (2) convolving with a homogeneous self-similar measure increases correlation dimension by a quantitative amount, (3) the dimension and Frostman exponent of (biased) Bernoulli convolutions tend to 1 as the contraction ratio tends to 1, at an explicit quantitative rate.
Fil: Mosquera, Carolina Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description R. Kaufman and M. Tsujii proved that the Fourier transform of self-similar measures has a power decay outside of a sparse set of frequencies. We present a version of this result for homogeneous self-similar measures, with quantitative estimates, and derive several applications: (1) non-linear smooth images of homogeneous self-similar measures have a power Fourier decay, (2) convolving with a homogeneous self-similar measure increases correlation dimension by a quantitative amount, (3) the dimension and Frostman exponent of (biased) Bernoulli convolutions tend to 1 as the contraction ratio tends to 1, at an explicit quantitative rate.
publishDate 2018
dc.date.none.fl_str_mv 2018-02
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/117954
Mosquera, Carolina Alejandra; Shmerkin, Pablo Sebastian; Self-similar measures: asymptotic bounds for the dimension and Fourier decay of smooth images; Suomalainen Tiedeakatemia; Annales Academiae Scientiarum Fennicae. Mathematica; 43; 2; 2-2018; 823-834
1239-629X
1798-2383
CONICET Digital
CONICET
url http://hdl.handle.net/11336/117954
identifier_str_mv Mosquera, Carolina Alejandra; Shmerkin, Pablo Sebastian; Self-similar measures: asymptotic bounds for the dimension and Fourier decay of smooth images; Suomalainen Tiedeakatemia; Annales Academiae Scientiarum Fennicae. Mathematica; 43; 2; 2-2018; 823-834
1239-629X
1798-2383
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.acadsci.fi/mathematica/
info:eu-repo/semantics/altIdentifier/url/http://www.acadsci.fi/mathematica/Vol43/FengKaenmaki.html
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/zip
application/pdf
dc.publisher.none.fl_str_mv Suomalainen Tiedeakatemia
publisher.none.fl_str_mv Suomalainen Tiedeakatemia
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.22299

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