7 problems

Let $G$ be a locally compact abelian group with separable dual group $\hat{G}$, and let $\varphi\in\mathcal{H}(G)$ be a Hartman measurable function. Write…

Let $\mathscr{G}$ be a locally compact abelian group and let $\widehat{\mathscr{G}}$ be its dual group. The modulation space $M^{\infty,1}(\mathscr{G}\times\widehat{\mathscr{G}})$…

A locally compact abelian group is a locally compact topological group whose group operation is commutative. Let $L^2(\G)$ denote the associated Hilbert space of square-integrable…

Universal KD-real span conjecture. The equality

Let $\mathcal{F}_\psi$ be the system of translates associated with a function $\psi$, and let $p_\psi$ be its periodization function on $\mathbb{T}$. Characterization conjecture. T…

Let $\mathcal{L}$ be a lattice and let $\mathcal{F}_\psi$ be the associated system of translates. A finite subset of $\mathcal{L}$ is an arithmetic progression when it has the form…

Let $G$ be either ${\mathbb R}$ or ${\mathbb T}$, and let $\Omega\subseteq G$ be a measurable set of fixed measure $|\Omega|=m$. A set is zero-symmetric when it is symmetric about…