4 problems

Gröchenig's conjecture. If $phi$ is totally positive and is not the one-sided exponential, then

Daubechies–Gröchenig conjecture. The system $\mathcal{G}(g,\alpha\mathbb{Z}\times\beta\mathbb{Z})$ is a Gabor frame for $L^2(\mathbb{R})$ if and only if

Let $g$ be a totally positive function, and let $\mathcal{G}(g,\alpha,\beta)$ denote its Gabor system with lattice parameters $\alpha,\beta$. The totally positive Gabor frame conje…

Modified conjecture. Every continuous totally positive function satisfies