On the Gibbs Properties of Bernoulli Convolutions Related to ß-Numeration in Multinacci Bases

• Autores: Eric Olivier, Nikita Sidorov, Alain Thomas
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 145, Nº 2, 2005, págs. 145-174
• Idioma: inglés
• DOI: 10.1007/s00605-005-0298-z
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• Resumen

  • We consider infinitely convolved Bernoulli measures (or simply Bernoulli convolutions) related to the -numeration. A matrix decomposition of these measures is obtained in the case when is a PV number. We also determine their Gibbs properties for being a multinacci number, which makes the multifractal analysis of the corresponding Bernoulli convolution possible.