2 problems

Let $\Gamma$ be a $C^4$-smooth, asymptotically straight planar curve. Let $\Sigma_{\alpha,\Gamma}(k)$ be the on-shell scattering matrix at energy $k^2$, and let $S_\Gamma$ be the o…

Let $\Gamma$ be a graph with some semi-infinite, asymptotically straight edges, and suppose … Consider the renormalized operator $-\Delta_{\alpha,\Gamma}+\frac14\alpha^2$ as…