4 problems

Conjugate-operator conjecture. There exists such a conjugate operator $\mathbb{A}(n)$ for which the Mourre estimate for $\Delta$ holds with respect to $\mathbb{A}(n)$ for every…

Three-dimensional Mourre conjecture. On every interval $(\mathcal{E}_n,\mathcal{E}_{n-1})$, the Mourre estimate holds with

Let $D$ be the discrete Molchanov–Vainberg Laplacian in dimension $2$, let $\kappa$ be even, and let $\mathcal{E}_{i_1},\mathcal{E}_{i_2}\in\boldsymbol{\Theta}_{\kappa}(D)$ be cons…

Fix $\kappa\geq4$ with $\kappa\in\mathbb{N}_e$, and let $\{\mathcal{E}_n\}$ be the sequence from the stated theorem. Let $A_{j\kappa}=\sum_{i=1}^{2}A_i(j,\kappa)$ be the conjugate…