5 problems

Let $\Lambda_\varphi$ be the one-dimensional Dirac operator on $L^2({\mathbb{R}},{\mathbb{C}}^2)$, with potential $\varphi:{\mathbb{R}}\to{\mathbb{C}}$ satisfying … Call…

Let $K(\gamma)$ be the Cantor-type set associated with $\gamma$, let $\mu_{K(\gamma)}$ be its associated measure, and let $W_n^2(\mu_{K(\gamma)})$ be the corresponding Widom–Hilber…

Let $K(\gamma)$ be the Cantor-type set determined by $\gamma$, and let $H_{\mu_{K(\gamma)}}$ have recurrence-coefficient sequence $(a_n)_{n=1}^\infty$. An almost periodic sequence…

Last's periodic approximation conjecture. For any $\alpha\notin\mathbb{Q}$, $\mathcal{A}(\alpha)=\lim_{p/q\to\alpha}S_-(p/q)$, in the sense that

Let $(\beta,A_\epsilon^E)$ be an analytic almost periodic Jacobi cocycle, and suppose that its determinant is bounded away from zero. Almost reducibility conjecture for Jacobi cocy…