2 problems

Let $K$ be an abstract Klein-Gordon operator on $L^2(\mathbb{R},\mathcal K)$, and let $R_z(t,s)$ and $\mathcal Z_{\pm,z}^{(\pm)}(t)$ be the evolution and asymptotic subspaces defin…

Let $G=(V,c,E)$ be the one-dimensional weighted graph considered above, with edge conductances $c_{n,n-1}=a_n$ and energy Hilbert space $\mathscr{H}_{E}$. Let $\Delta$ denote the c…