4 problems

Given a number $\beta\in(1,2)$, let $\nu_{\beta}$ denote the associated Bernoulli convolution and let $\dim_H$ denote Hausdorff dimension. Large-degree Pisot dimension conjecture.…

Let $\nu_{\beta_1}$ denote the Bernoulli convolution associated with $\beta_1$. Suppose that $\beta_1\in(1,2)$, $\beta_1\neq(1+\sqrt{5})/2$, and that $\beta_1$ has a real conjugate…

Dimension-one conjecture. Under these assumptions,

Let $\nu_{\beta}$ be the Bernoulli convolution associated with $\beta$, and let $f_n$ denote the sequence of approximating functions introduced in the paper. Convergence conjecture…