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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/117484
Ver los metadatos del registro completo
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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 Técnicas2025-09-29T10:16:34Zoai: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:34982025-09-29 10:16:34.358CONICET 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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1844614111953944576 |
score |
13.070432 |