4 problems

Let $Q_2=Q_1*Q_1$, where $Q_1(x):=\chi_{[-1/2,1/2]}(x)$, and let $\mathcal{G}(Q_2,a,b)$ denote the associated Gabor system. Nielsen's conjecture. The Gabor system…

Lemvig and Nielsen's conjecture. The Gabor system $\mathcal{G}(Q_2,a,b)$ is not a frame along the hyperbolas

Non-frame conjecture. The Gabor system $\mathcal{G}(B_2,a_0,b_0)$ is not a frame. Furthermore, it is not a frame along the hyperbolas

Let $C_m^d$ be the circulant associated with the degree-$d$ B-spline collocation matrix, with Toeplitz symbol coefficients $t_0^d,\ldots,t_r^d$, and let $\lambda_\mu(C_m^d)$ denote…