Absolute continuity of complex Bernoulli convolutions

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 me...

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Detalles Bibliográficos
Autores: Shmerkin, Pablo Sebastian, Solomyak, Boris
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2016
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/46816
Acceso en línea:http://hdl.handle.net/11336/46816
Access Level:acceso abierto
Palabra clave:BERNOULLI CONVOLUTIONS
SELF-SIMILAR MEASURES
ABSOLUTE CONTINUITY
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario: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.