4 problems

Let $D$ be a two- or three-dimensional obstacle, let $x$ lie in its exterior, and write $r=|x|$ and $\alpha'=x/r$. Let $u(x,\alpha)$ be the acoustic field for an incident plane wav…

The Rayleigh conjecture. The series above converges up to the boundary $S$.

Diagonal-dominance conjecture. The matrix $\{\delta_{m'm}-c_{m'm}\}_{m',m=0}^{\infty}$ remains diagonally dominant; consequently, ${\cal I}-{\cal A}_h$ should have a bounded invers…

Let $G$ be the dissipative acoustic operator, and let $(\lambda_k)$ be a sequence of its eigenvalues. Unbounded-imaginary-part conjecture. There exists a sequence of eigenvalues…