From Sommerfeld Diffraction Problems to Operator Factorisation

Abstract

This article presents a brief survey devoted to the interplay between diffraction and operator theory,particularly between the so-called canonical diffraction problems (exemplified by Sommerfeld half-plane problems) onone hand and operator factorisation theory on the other hand. It is shown how operator factorisation concepts appearin a natural way from applications and how they can help to find solutions rigorously in case of well-posed problemsor how to normalise problems by an adequate change of function spaces.