3 problems

Let $\mathcal{G}_N(\phi_i,\Lambda_i)$ be a Gabor system in $L^2(\mathbb{R}^d)$, where the disjoint union $\bigcup_{i=1}^N\Lambda_i$ is formed from the parameter sets…

Affirmative Beurling density conjecture. For every $(t,s)\in(0,\frac{1}{2}]\times[0,\infty)$, there exists a spectrum $Lambda:= Lambda{t,s}$ of $mu{4,{0,2}}$ such that

Beurling-density upper-bound conjecture. For any maximal orthogonal set $\Lambda$ of $\mu_{p,q}$,