9 problems

Let $\Sigma\subset \mathbb{R}^d$ be a compact set that is not a removable set for $\Delta$ in $L^2(\mathbb{R}^d)$. A self-adjoint extension of…

Point-spectrum conjecture. One has $\alpha\in\sigma_p(\widetilde A)$ if and only if either there exists a nontrivial element $y_0$ such that

Let $T$ be a Hermitian linear operator with lower bound $C$, and let $C'<C$. Von Neumann's result guarantees a self-adjoint extension of $T$ that is semibounded with lower bound…

Let ${\bf L}^n_0$, with $n\in\mathbb{N}$, be a self-adjoint extension of the minimal operator $L^n_{\scriptstyle \text{min}}$ on $L^2[(a,b),w]$, with deficiency indices $(m,m)$ whe…

Let $E_q$ be the fiber at a boundary point $q$, let $E_{f(q)}$ be the fiber at its image under the boundary map $f$, and set … For boundary data … let $\widetilde{A}$ be the self-a…

Complete Lagrangian boundary-condition conjecture. The boundary condition

Zero-mode conjecture. Only one linear combination of $\psi_0^B$ and $\psi_0^F$ is a zero mode of $A$ for each choice of self-adjoint extension of $Q$.

Let $k\in\mathbb{R}$ be arbitrary. Consider a quantum mechanical particle in $\mathbb{R}^3$ under the inverse square potential $k|x|^{-2}$, and let $\ell$ denote its orbital quantu…

Speed-dependence conjecture. This physical difference between the Schrödinger and Dirac particles depends on the speed of the particle.