5 problems

Let $\mu_{\rho,d}$ be the Bernoulli convolution with contraction parameter $0<\rho\le1/2$ and scale parameter $d>0$. A measure is spectral when its associated $L^2$ space admits an…

Non-frame-spectrality conjecture for $\mu_4+\mu_8$. The measure $\mu_4+\mu_8$ is not frame-spectral.

Translational absolute continuity conjecture. If $\mu$ is a frame-spectral measure, then $\mu$ must be translationally absolutely continuous.

Let $R$ be a $d\times d$ expansive integer matrix, and let $B\subset\mathbb{Z}^d$ contain $0$, with the elements of $B$ mutually incongruent modulo $R$. Suppose there are a set…

Let $(N_j,B_j)$ be the almost-Parseval-frame tower defined in Theorem 0.1, and let $bc$ be its associated measure. The measure $bc$ is spectral if there exists a set…