Abstract:
It was shown by Ascenzi, Lyubarskii, Seip that the upper density of any complete and minimal system of Gaussians is between $\frac{2}{\pi}$ and 1, if we know that there exists an angular density. It was an open question whether it is true in general. We will show that there exists a complete and minimal system with upper density $\dfrac{1}{\pi}$, and that the uppper density of any such system is larger than $\dfrac{1}{3\pi}$. The talk is based on work in collaboration with A. Borichev and A. Kuznetsov.
