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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/117954
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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 Técnicas2025-09-29T09:55:18Zoai: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:34982025-09-29 09:55:19.166CONICET 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 |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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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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1844613668638031872 |
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13.070432 |