Cospectral trees indistinguishable by scattering

Mats-Erik Pistol, Vyacheslav Pivovarchik

Let v_1 and v_2 be two distinct vertices of a tree T_0. Let ϕ_N^{(i)} (i=1,2) be the characteristic functions of the Sturm-Liouville problem on T_0 rooted at v_i with Neumann cond…