On a limiting absorption principle for sesquilinear forms with an application to the Helmholtz equation in a waveguide
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Date
2019-04
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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 .