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...
| Autores: | , |
|---|---|
| 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 |
| 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. |
|---|