3 problems

Let $l,g$ be two even functions with $g>0$ on $(0,\pi)$, and suppose that $f\equiv l/g$ is monotone increasing over $(0,\pi)$. Set $X_n\equiv T_n^{-1}(g)T_n(l)$ for all $n$. Let…

Let $\{\tilde{\sigma}_j\}_{j\in\mathbb N_0}$ be the edge-wave and surface-wave quasi-eigenvalues arranged in ascending order. The sequence is asymptotically complete if the indexin…

Let $N(c3)$ be the eigenvalue counting function of the sloshing problem, and let $N^e(c3)$ and $N^s(c3)$ denote respectively the counting functions for edge-wave and surface-wave q…