Absolute continuity of complex Bernoulli convolutions

Autores
Shmerkin, Pablo Sebastian; Solomyak, Boris
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We prove that complex Bernoulli convolutions are absolutely continuous in the supercritical parameter region, outside of an exceptional set of parameters of zero Hausdorff dimension. Similar results are also obtained in the biased case, and for other parametrised families of self-similar sets and measures in the complex plane, extending earlier results.
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. Bar Ilan University; Israel
Materia
BERNOULLI CONVOLUTIONS
SELF-SIMILAR MEASURES
ABSOLUTE CONTINUITY
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:11336/46816
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Absolute continuity of complex Bernoulli convolutionsShmerkin, Pablo SebastianSolomyak, BorisBERNOULLI CONVOLUTIONSSELF-SIMILAR MEASURESABSOLUTE CONTINUITYhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We prove that complex Bernoulli convolutions are absolutely continuous in the supercritical parameter region, outside of an exceptional set of parameters of zero Hausdorff dimension. Similar results are also obtained in the biased case, and for other parametrised families of self-similar sets and measures in the complex plane, extending earlier results.Fil: Shmerkin, Pablo Sebastian. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Solomyak, Boris. Bar Ilan University; IsraelCambridge University Press2016-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/46816Shmerkin, Pablo Sebastian; Solomyak, Boris; Absolute continuity of complex Bernoulli convolutions; Cambridge University Press; Mathematical Proceedings Of The Cambridge Philosophical Society; 161; 3; 11-2016; 435-4530305-0041CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1017/S0305004116000335info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1504.00631info:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society/article/absolute-continuity-of-complex-bernoulli-convolutions/C81F2BDC7B61460541F3AD24158DC2CCinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:34:02Zoai:ri.conicet.gov.ar:11336/46816instacron: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 09:34:02.516CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Absolute continuity of complex Bernoulli convolutions
title Absolute continuity of complex Bernoulli convolutions
spellingShingle Absolute continuity of complex Bernoulli convolutions
Shmerkin, Pablo Sebastian
BERNOULLI CONVOLUTIONS
SELF-SIMILAR MEASURES
ABSOLUTE CONTINUITY
title_short Absolute continuity of complex Bernoulli convolutions
title_full Absolute continuity of complex Bernoulli convolutions
title_fullStr Absolute continuity of complex Bernoulli convolutions
title_full_unstemmed Absolute continuity of complex Bernoulli convolutions
title_sort Absolute continuity of complex Bernoulli convolutions
dc.creator.none.fl_str_mv Shmerkin, Pablo Sebastian
Solomyak, Boris
author Shmerkin, Pablo Sebastian
author_facet Shmerkin, Pablo Sebastian
Solomyak, Boris
author_role author
author2 Solomyak, Boris
author2_role author
dc.subject.none.fl_str_mv BERNOULLI CONVOLUTIONS
SELF-SIMILAR MEASURES
ABSOLUTE CONTINUITY
topic BERNOULLI CONVOLUTIONS
SELF-SIMILAR MEASURES
ABSOLUTE CONTINUITY
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 complex Bernoulli convolutions are absolutely continuous in the supercritical parameter region, outside of an exceptional set of parameters of zero Hausdorff dimension. Similar results are also obtained in the biased case, and for other parametrised families of self-similar sets and measures in the complex plane, extending earlier results.
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. Bar Ilan University; Israel
description We prove that complex Bernoulli convolutions are absolutely continuous in the supercritical parameter region, outside of an exceptional set of parameters of zero Hausdorff dimension. Similar results are also obtained in the biased case, and for other parametrised families of self-similar sets and measures in the complex plane, extending earlier results.
publishDate 2016
dc.date.none.fl_str_mv 2016-11
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/11336/46816
Shmerkin, Pablo Sebastian; Solomyak, Boris; Absolute continuity of complex Bernoulli convolutions; Cambridge University Press; Mathematical Proceedings Of The Cambridge Philosophical Society; 161; 3; 11-2016; 435-453
0305-0041
CONICET Digital
CONICET
url http://hdl.handle.net/11336/46816
identifier_str_mv Shmerkin, Pablo Sebastian; Solomyak, Boris; Absolute continuity of complex Bernoulli convolutions; Cambridge University Press; Mathematical Proceedings Of The Cambridge Philosophical Society; 161; 3; 11-2016; 435-453
0305-0041
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1017/S0305004116000335
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1504.00631
info:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society/article/absolute-continuity-of-complex-bernoulli-convolutions/C81F2BDC7B61460541F3AD24158DC2CC
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/pdf
dc.publisher.none.fl_str_mv Cambridge University Press
publisher.none.fl_str_mv Cambridge University Press
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 13.070432

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