Sectorial Hamiltonians without zero resonance in one dimension

摘要

We consider a 1-D Laplace operator with short range potential W(x) and study sectorial properties and resolvent estimates associated with this perturbed Laplacian. It is shown that non resonance assumption at zero and sufficiently fast decay of the potential at infinity guarantee that the Hamiltonian is a sectorial operator in L~p for 1 < p ≤ ∞.