5 problems

Higher-dimensional asymptotic conjecture. A similar asymptotic formula should remain valid with the effective potential replaced by the function of the principal curvatures derived…

Let $\Sigma$ be the generalized paraboloid supporting a self-adjoint three-dimensional Schrödinger operator with an attractive $\delta$-interaction of constant strength. Let…

Tubular Dirichlet approximation conjecture. Since the eigenfunctions of $H$ decay fast with the distance from $S$, the eigenvalues of $H$ are close to those of $K_\varepsilon$ in a…

Let $S$ be a smooth surface with boundary supporting an attractive delta-interaction of coupling strength $\beta$, and let the strong-coupling eigenvalue asymptotics be described b…

Consider the one-dimensional Hamiltonian … where $Y=\{y_1,\dots,y_n\}$ consists of mutually distinct points and the coupling constants satisfy $\alpha_j<0$ for $j=1,\dots,n$. Its g…