3 problems

Modified Łaba–Wang conjecture. If $\mu_{\rho,\mathcal{D},{\bf p}}$ is a spectral measure, then ${\bf p}$ is equal-weight, with $p_j=1/m$; $\rho=1/N$ for some integer $N\geq2$; and…

Let $N\ge 2$ be a positive integer, let $\mathcal{D}$ be a digit set defining the self-similar measure $mu_{N,\mathcal{D}}$, and let a product-form Hadamard triple with respect to…

Let $M\in M_n(\mathbb{Z})$ be an expanding matrix and let $D\subset\mathbb{Z}^n$ be a finite set. A Hadamard triple is a triple $(M,D,S)$, where $S\subset\mathbb{Z}^n$ is finite wi…