3 problems

Let $S\subset\mathbb R^n$. A set of injectivity for the spherical means for $C_c(\mathbb R^2)$ is a set such that, for every $f$ in that class, $f\ast\mu_r(x)=0$ for all $r>0$ and…

Let $S\subset\mathbb R^d$. Call $S$ an injectivity set for the spherical mean transform if vanishing of all spherical means centered on $S$ forces the underlying function or distri…

Let $\mu_r$ denote the normalized surface measure on the circle of radius $r$ in $\mathbb C$, let $\omega$ be an $N$th root of unity, and let … For $f\in L^2(\mathbb C)$, vanishing…