Absolute continuity of non-homogeneous self-similar measures

Autores
Saglietti, Santiago Juan; Shmerkin, Pablo Sebastian; Solomyak, Boris
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We prove that self-similar measures on the real line are absolutely continuous for almost all parameters in the super-critical region, in particular confirming a conjecture of S.-M. Ngai and Y. Wang. While recently there has been much progress in understanding absolute continuity for homogeneous self-similar measures, this is the first improvement over the classical transversality method in the general (non-homogeneous) case. In the course of the proof, we establish new results on the dimension and Fourier decay of a class of random self-similar measures.
Fil: Saglietti, Santiago Juan. Technion - Israel Institute of Technology; Israel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Solomyak, Boris. No especifíca;
Materia
ABSOLUTE CONTINUITY
CONVOLUTIONS
RANDOM MEASURES
SELF-SIMILAR MEASURES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/117484
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/117484
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Absolute continuity of non-homogeneous self-similar measuresSaglietti, Santiago JuanShmerkin, Pablo SebastianSolomyak, BorisABSOLUTE CONTINUITYCONVOLUTIONSRANDOM MEASURESSELF-SIMILAR MEASUREShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We prove that self-similar measures on the real line are absolutely continuous for almost all parameters in the super-critical region, in particular confirming a conjecture of S.-M. Ngai and Y. Wang. While recently there has been much progress in understanding absolute continuity for homogeneous self-similar measures, this is the first improvement over the classical transversality method in the general (non-homogeneous) case. In the course of the proof, we establish new results on the dimension and Fourier decay of a class of random self-similar measures.Fil: Saglietti, Santiago Juan. Technion - Israel Institute of Technology; Israel. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Solomyak, Boris. No especifíca;Academic Press Inc Elsevier Science2018-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/117484Saglietti, Santiago Juan; Shmerkin, Pablo Sebastian; Solomyak, Boris; Absolute continuity of non-homogeneous self-similar measures; Academic Press Inc Elsevier Science; Advances in Mathematics; 335; 9-2018; 60-1100001-8708CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://linkinghub.elsevier.com/retrieve/pii/S0001870818302469info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aim.2018.06.015info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:46:44Zoai:ri.conicet.gov.ar:11336/117484instacron: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:34982025-10-22 11:46:44.365CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Absolute continuity of non-homogeneous self-similar measures
title Absolute continuity of non-homogeneous self-similar measures
spellingShingle Absolute continuity of non-homogeneous self-similar measures
Saglietti, Santiago Juan
ABSOLUTE CONTINUITY
CONVOLUTIONS
RANDOM MEASURES
SELF-SIMILAR MEASURES
title_short Absolute continuity of non-homogeneous self-similar measures
title_full Absolute continuity of non-homogeneous self-similar measures
title_fullStr Absolute continuity of non-homogeneous self-similar measures
title_full_unstemmed Absolute continuity of non-homogeneous self-similar measures
title_sort Absolute continuity of non-homogeneous self-similar measures
dc.creator.none.fl_str_mv Saglietti, Santiago Juan
Shmerkin, Pablo Sebastian
Solomyak, Boris
author Saglietti, Santiago Juan
author_facet Saglietti, Santiago Juan
Shmerkin, Pablo Sebastian
Solomyak, Boris
author_role author
author2 Shmerkin, Pablo Sebastian
Solomyak, Boris
author2_role author
author
dc.subject.none.fl_str_mv ABSOLUTE CONTINUITY
CONVOLUTIONS
RANDOM MEASURES
SELF-SIMILAR MEASURES
topic ABSOLUTE CONTINUITY
CONVOLUTIONS
RANDOM MEASURES
SELF-SIMILAR MEASURES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We prove that self-similar measures on the real line are absolutely continuous for almost all parameters in the super-critical region, in particular confirming a conjecture of S.-M. Ngai and Y. Wang. While recently there has been much progress in understanding absolute continuity for homogeneous self-similar measures, this is the first improvement over the classical transversality method in the general (non-homogeneous) case. In the course of the proof, we establish new results on the dimension and Fourier decay of a class of random self-similar measures.
Fil: Saglietti, Santiago Juan. Technion - Israel Institute of Technology; Israel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Solomyak, Boris. No especifíca;
description We prove that self-similar measures on the real line are absolutely continuous for almost all parameters in the super-critical region, in particular confirming a conjecture of S.-M. Ngai and Y. Wang. While recently there has been much progress in understanding absolute continuity for homogeneous self-similar measures, this is the first improvement over the classical transversality method in the general (non-homogeneous) case. In the course of the proof, we establish new results on the dimension and Fourier decay of a class of random self-similar measures.
publishDate 2018
dc.date.none.fl_str_mv 2018-09
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/11336/117484
Saglietti, Santiago Juan; Shmerkin, Pablo Sebastian; Solomyak, Boris; Absolute continuity of non-homogeneous self-similar measures; Academic Press Inc Elsevier Science; Advances in Mathematics; 335; 9-2018; 60-110
0001-8708
CONICET Digital
CONICET
url http://hdl.handle.net/11336/117484
identifier_str_mv Saglietti, Santiago Juan; Shmerkin, Pablo Sebastian; Solomyak, Boris; Absolute continuity of non-homogeneous self-similar measures; Academic Press Inc Elsevier Science; Advances in Mathematics; 335; 9-2018; 60-110
0001-8708
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://linkinghub.elsevier.com/retrieve/pii/S0001870818302469
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aim.2018.06.015
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
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 12.982451

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