7 problems

Let $\widetilde\nu$ be the Cantor measure pushed forward to $(0,1)$, let $H_{M-1}=\sum_{n=1}^{M-1}n^{-1}$ be the harmonic number, and set $M=\lfloor\sqrt t\rfloor$. Cantor-weighted…

Let $\nu$ be the Cantor measure used in the paper and let $\widetilde\nu$ be its pushforward to $(0,1)$. Let $\zeta(s,\alpha)$ denote the Hurwitz zeta function. Cantor-weighted Hur…

Suppose that $\mu$ is an Ahlfors--David regular probability measure supported on $[1,2]$ and satisfying … for $r<\operatorname{diam}(\operatorname{supp}\mu)$. Rough local smoothing…

Bell–Ho–Strichartz conjecture. As $m\to\infty$, the law of $r\circ c^{(w)}$ under $\lambda_m$ converges to the Dirac measure at $\sqrt{8/75}$, while the law of…

Let $\mu$ be an absolutely continuous probability measure supported on $[0,1]$ with density $f$. Assume there exist $C>0$ and $p>1$ such that, for all $0<r<R<1$ and $x$ in the supp…

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…

Let $\mu$ be a finite Borel measure on $\mathbb{R}^d$. Say that $\mu$ is translationally absolutely continuous if, for every Borel set $F$ in the support of $\mu$ with $\mu(F)>0$ a…