On the Limiting Absorption Principle for Schr{\"o}dinger operators on waveguides

Abstract

We prove a Limiting Absorption Principle for Schr{\"o}dinger operators in tubes about infinite curves embedded in the Euclidian space with different types of boundary conditions. The argument is based on the Mourre theory with conjugate operators different from the generator of dilations which is usually used in this case, and permits to prove a Limiting Absorption Principle for Schr{\"o}dinger operators in singular waveguides.