Long time quantum evolution of observables on cusp manifolds (Q273210)

Let \(M\) be a non-compact complete manifold of finite volume with hyperbolic ends (so called cusp manifolds). The Eisenstein functions are generalized eigenfunctions of the corresponding Laplacian on \(M\). In the paper, a version of quantum unique ergodicity for these functions is proved. For this purpose a semi-classical pseudo-differential calculus adapted to a geometrical class of symbols is built.