We introduce a parameter space containing all algebraic integers
β∈(1,2] that are not Pisot or Salem numbers, and a sequence of
increasing piecewise continuous function on this parameter space which gives a
lower bound for the Garsia entropy of the Bernoulli convolution νβ​.
This allows us to show that dimH​(νβ​)=1 for all
β with representations in certain open regions of the parameter space.Comment: 21 pages, 2 figures, 5 table