On a Limiting Absorption Principle for Sesquilinear Forms with an Application to the Helmholtz Equation in a Waveguide

Abstract

We prove a limiting absorption principle for sesquilinear forms on Hilbert spaces and apply the abstract result to a Helmholtz equation with radiation condition. The limiting absorption principle is based on a Fredholm alternative. It is applied to Helmholtz-type equations in a truncated waveguide geometry. We analyse a problem with radiation conditions on truncated domains, recently introduced in [4]. We improve the previous results by treating the limit δ → 0.