From Sommerfeld Diffraction Problems to Operator Factorisation

Year 2019, , 183 - 216, 01.12.2019

Frank - Olme Speck

https://doi.org/10.33205/cma.620578

Cited By: 2

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) on one hand and operator factorisation theory on the other hand. It is shown how operator factorisation concepts appear in a natural way from applications and how they can help to find solutions rigorously in case of well-posed problems or how to normalize problems by an adequate change of function spaces.

Keywords

Sommerfeld problem, diffraction, Wiener-Hopf method, Wiener- Hopf operator, factorisation, intermediate space, generalised inverse, op- erator relation

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