Counting-expansions and the absolute continuity of Bernoulli convolutions
T Kempton - Monatshefte für Mathematik, 2013 - Springer
Monatshefte für Mathematik, 2013•Springer
We study the typical growth rate of the number of words of length n which can be extended
to β-expansions of x. In the general case we give a lower bound for the growth rate, while in
the case that the Bernoulli convolution associated to parameter β is absolutely continuous
we are able to give the growth rate precisely. This gives new necessary and sufficient
conditions for the absolute continuity of Bernoulli convolutions.
to β-expansions of x. In the general case we give a lower bound for the growth rate, while in
the case that the Bernoulli convolution associated to parameter β is absolutely continuous
we are able to give the growth rate precisely. This gives new necessary and sufficient
conditions for the absolute continuity of Bernoulli convolutions.
Abstract
We study the typical growth rate of the number of words of length which can be extended to -expansions of . In the general case we give a lower bound for the growth rate, while in the case that the Bernoulli convolution associated to parameter is absolutely continuous we are able to give the growth rate precisely. This gives new necessary and sufficient conditions for the absolute continuity of Bernoulli convolutions.
Springer