A MOURRE ESTIMATE FOR A SCHRÖDINGER OPERATOR ON A BINARY TREE

Source abstract

Let G be a binary tree with vertices V and H be a Schrödinger operator acting on ℓ 2 (V). A decomposition of the space ℓ 2 (V) into invariant subspaces is exhibited yielding a conjugate operator A for use in the Mourre estimate. We show that for potentials q satisfying a first order difference decay condition, a Mourre estimate for H holds.